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href="/w/index.php?title=Toiminnot:Tuoreet_muutokset&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin-vector-legacy mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Konjunktio_logiikka rootpage-Konjunktio_logiikka skin-vector action-view"><div id="mw-page-base" class="noprint"></div> <div id="mw-head-base" class="noprint"></div> <div id="content" class="mw-body" role="main"> <a id="top"></a> <div id="siteNotice"></div> <div class="mw-indicators"> </div> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Konjunktio (logiikka)</span></h1> <div id="bodyContent" class="vector-body"> <div id="siteSub" class="noprint">Wikipediasta</div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="contentSub2"></div> <div id="jump-to-nav"></div> <a class="mw-jump-link" href="#mw-head">Siirry navigaatioon</a> <a class="mw-jump-link" href="#searchInput">Siirry hakuun</a> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="fi" dir="ltr"><figure typeof="mw:File/Thumb"><a href="/wiki/Tiedosto:Venn0001.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Venn0001.svg/220px-Venn0001.svg.png" decoding="async" width="220" height="160" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Venn0001.svg/330px-Venn0001.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Venn0001.svg/440px-Venn0001.svg.png 2x" data-file-width="410" data-file-height="299" /></a><figcaption>Lausetta <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle A\land B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>A</mi> <mo>∧</mo> <mi>B</mi> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle A\land B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f8365200c858ceecb1357b8336aaec576cc379e9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.576ex; height:1.843ex;" alt="{\displaystyle \scriptstyle A\land B}"></span> vastaava <a href="/wiki/Venn-diagrammi" title="Venn-diagrammi">Venn-diagrammi</a></figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/Tiedosto:Venn_0000_0001.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Venn_0000_0001.svg/220px-Venn_0000_0001.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Venn_0000_0001.svg/330px-Venn_0000_0001.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Venn_0000_0001.svg/440px-Venn_0000_0001.svg.png 2x" data-file-width="200" data-file-height="200" /></a><figcaption>Lausetta <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle A\land B\land C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <mi>A</mi> <mo>∧</mo> <mi>B</mi> <mo>∧</mo> <mi>C</mi> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle A\land B\land C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8805277a42035a76e462c87444eeb65562e811da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.921ex; height:1.843ex;" alt="{\displaystyle \scriptstyle A\land B\land C}"></span> vastaava Venn-diagrammi</figcaption></figure> <p><b>Konjunktio</b> on <a href="/wiki/Propositiologiikka" title="Propositiologiikka">propositiologiikassa</a> kaksipaikkainen <a href="/wiki/Looginen_konnektiivi" class="mw-redirect" title="Looginen konnektiivi">looginen konnektiivi</a>, joka vastaa yleiskielen sanaa <i>ja</i>. Sillä muodostettu yhdistetty lause on tosi, jos molemmat sen yhdistämät lauseet ovat tosia, muussa tapauksessa epätosi. Lauseiden <i>A</i> ja <i>B</i> konjunktiolle käytetään merkintää <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\land B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>∧</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\land B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74954195333a8593163b93a9688695b8dc74da55" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.09ex; height:2.176ex;" alt="{\displaystyle A\land B}"></span>. </p><p>Konjunktioon läheisesti liittyviä käsitteitä muissa yhteyksissä ovat: </p> <ul><li><a href="/wiki/Joukko-oppi" title="Joukko-oppi">joukko-opissa</a> <a href="/wiki/Leikkaus_(matematiikka)" title="Leikkaus (matematiikka)">leikkaus</a></li> <li><a href="/wiki/Predikaattilogiikka" title="Predikaattilogiikka">predikaattilogiikassa</a> <a href="/wiki/Universaalikvanttori" title="Universaalikvanttori">universaalikvanttori</a> eli kaikki-kvanttori</li> <li><a href="/wiki/Elektroniikka" title="Elektroniikka">elektroniikassa</a> konjunktiota vastaa <a href="/wiki/AND-portti" title="AND-portti">AND-portti</a>.</li></ul> <div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none" /><div class="toctitle" lang="fi" dir="ltr"><h2 id="mw-toc-heading">Sisällys</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span></div> <ul> <li class="toclevel-1 tocsection-1"><a href="#Merkinnät"><span class="tocnumber">1</span> <span class="toctext">Merkinnät</span></a></li> <li class="toclevel-1 tocsection-2"><a href="#Totuustaulu"><span class="tocnumber">2</span> <span class="toctext">Totuustaulu</span></a></li> <li class="toclevel-1 tocsection-3"><a href="#Ominaisuudet"><span class="tocnumber">3</span> <span class="toctext">Ominaisuudet</span></a></li> <li class="toclevel-1 tocsection-4"><a href="#Sovellukset_tietotekniikassa"><span class="tocnumber">4</span> <span class="toctext">Sovellukset tietotekniikassa</span></a> <ul> <li class="toclevel-2 tocsection-5"><a href="#Biteittäinen_operaatio"><span class="tocnumber">4.1</span> <span class="toctext">Biteittäinen operaatio</span></a></li> </ul> </li> <li class="toclevel-1 tocsection-6"><a href="#Leikkaus"><span class="tocnumber">5</span> <span class="toctext">Leikkaus</span></a></li> <li class="toclevel-1 tocsection-7"><a href="#Luonnolliset_kielet"><span class="tocnumber">6</span> <span class="toctext">Luonnolliset kielet</span></a></li> <li class="toclevel-1 tocsection-8"><a href="#Katso_myös"><span class="tocnumber">7</span> <span class="toctext">Katso myös</span></a></li> <li class="toclevel-1 tocsection-9"><a href="#Lähteet"><span class="tocnumber">8</span> <span class="toctext">Lähteet</span></a></li> <li class="toclevel-1 tocsection-10"><a href="#Aiheesta_muualla"><span class="tocnumber">9</span> <span class="toctext">Aiheesta muualla</span></a></li> </ul> </div> <div class="mw-heading mw-heading2"><h2 id="Merkinnät"><span id="Merkinn.C3.A4t"></span>Merkinnät</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Konjunktio_(logiikka)&veaction=edit&section=1" title="Muokkaa osiota Merkinnät" class="mw-editsection-visualeditor"><span>muokkaa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Konjunktio_(logiikka)&action=edit&section=1" title="Muokkaa osion lähdekoodia: Merkinnät"><span>muokkaa wikitekstiä</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Loogiselle konjunktiolle käytetään kirjallisuudessa useita eri symboleja. Sanan "ja" (<a href="/wiki/Englannin_kieli" title="Englannin kieli">engl.</a> <span lang="en"><i>and</i></span>) ohella sille käytetään yleisesti symbolia "<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \land }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \land }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6823e5a222eb3ca49672818ac3d13ec607052c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \land }"></span>",<sup id="cite_ref-Hazewinkel_1-0" class="reference"><a href="#cite_note-Hazewinkel-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Esimerkiksi "<i>A</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \land }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \land }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6823e5a222eb3ca49672818ac3d13ec607052c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \land }"></span> <i>B</i> " luetaan "<i>A</i> ja <i>B</i>". Tällainen konjunktio on tosi vain jos sekä <i>A</i> että <i>B</i> ovat tosia lauseita, muussa tapauksessa se on epätosi. </p><p>Kaikki seuraavat ovat konjunktiota: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\land B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>∧</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\land B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74954195333a8593163b93a9688695b8dc74da55" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.09ex; height:2.176ex;" alt="{\displaystyle A\land B}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \neg A\land B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">¬</mi> <mi>A</mi> <mo>∧</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \neg A\land B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/475f4fcd67189aefd0849ac56030d0e1682c0be8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.64ex; height:2.176ex;" alt="{\displaystyle \neg A\land B}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\land \neg B\land \neg C\land D\land \neg E.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>∧</mo> <mi mathvariant="normal">¬</mi> <mi>B</mi> <mo>∧</mo> <mi mathvariant="normal">¬</mi> <mi>C</mi> <mo>∧</mo> <mi>D</mi> <mo>∧</mo> <mi mathvariant="normal">¬</mi> <mi>E</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\land \neg B\land \neg C\land D\land \neg E.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00ef21ecfe691d32b66e26233a5d0adf48baa086" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:24.602ex; height:2.176ex;" alt="{\displaystyle A\land \neg B\land \neg C\land D\land \neg E.}"></span></dd></dl> <p><a href="/wiki/Boolen_algebra" title="Boolen algebra">Boolen algebrassa</a> konjunktiolle käytetään merkintää <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A+B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>+</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A+B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4279cdbd3cb8ec4c3423065d9a7d83a82cfc89e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:6.348ex; height:2.343ex;" alt="{\displaystyle A+B}"></span>. <a href="/w/index.php?title=Jan_Lukasiewicz&action=edit&redlink=1" class="new" title="Jan Lukasiewicz (sivua ei ole)">Jan Lukasiewiczin</a> <a href="/w/index.php?title=Puolalainen_notaatio&action=edit&redlink=1" class="new" title="Puolalainen notaatio (sivua ei ole)">prefiksinotaatiossa</a> disjunktion merkkinä käytetään K-kirjainta, joka on lyhenne <a href="/wiki/Puolan_kieli" title="Puolan kieli">puolan kielen</a> sanasta <i>koniunkcja</i>. Tällöin lauseiden <i>p</i> ja <i>q</i> konjunktio merkitään K<i>pq</i>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>Eri <a href="/wiki/Ohjelmointikieli" title="Ohjelmointikieli">ohjelmointikielissä</a> konjunktiota vastaava operaattori merkitään tavallisimmin joko sanalla <code>and</code> tai kahdella <a href="/wiki/Et-merkki" class="mw-redirect" title="Et-merkki">et-merkillä</a> (<code>&&</code>). </p> <div class="mw-heading mw-heading2"><h2 id="Totuustaulu">Totuustaulu</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Konjunktio_(logiikka)&veaction=edit&section=2" title="Muokkaa osiota Totuustaulu" class="mw-editsection-visualeditor"><span>muokkaa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Konjunktio_(logiikka)&action=edit&section=2" title="Muokkaa osion lähdekoodia: Totuustaulu"><span>muokkaa wikitekstiä</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Tiedosto:Variadic_logical_AND.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Variadic_logical_AND.svg/250px-Variadic_logical_AND.svg.png" decoding="async" width="250" height="201" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Variadic_logical_AND.svg/375px-Variadic_logical_AND.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Variadic_logical_AND.svg/500px-Variadic_logical_AND.svg.png 2x" data-file-width="1807" data-file-height="1452" /></a><figcaption>Vasemmalla olevien argumenttien konjunktiot: arvon tosi saavat <a href="/wiki/Bitti" title="Bitti">bitit</a> muodostavat <a href="/wiki/Sierpinskin_kolmio" class="mw-redirect" title="Sierpinskin kolmio">Sierpinskin kolmion</a>.</figcaption></figure> <p>Operaation <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ~A\land B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>A</mi> <mo>∧</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ~A\land B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ffc52129283289ffc1479f098112ff8712ed007" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.67ex; height:2.176ex;" alt="{\displaystyle ~A\land B}"></span> <a href="/wiki/Totuustaulu" title="Totuustaulu">totuustaulu</a> on seuraava:<sup id="cite_ref-Hazewinkel_1-1" class="reference"><a href="#cite_note-Hazewinkel-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <table class="wikitable" style="margin: 0 0 1em 1em"> <tbody><tr bgcolor="#ddeeff" align="center"> <td colspan="2"><b>LAUSEET</b></td> <td><b>KONJUNKTIO</b> </td></tr> <tr bgcolor="#ddeeff" align="center"> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\land B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>∧</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\land B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74954195333a8593163b93a9688695b8dc74da55" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.09ex; height:2.176ex;" alt="{\displaystyle A\land B}"></span> </td></tr> <tr bgcolor="#ddffdd" align="center"> <td>tosi</td> <td>tosi</td> <td>tosi </td></tr> <tr bgcolor="#ddffdd" align="center"> <td>tosi</td> <td>epätosi</td> <td>epätosi </td></tr> <tr bgcolor="#ddffdd" align="center"> <td>epätosi</td> <td>tosi</td> <td>epätosi </td></tr> <tr bgcolor="#ddffdd" align="center"> <td>epätosi</td> <td>epätosi</td> <td>epätosi </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Ominaisuudet">Ominaisuudet</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Konjunktio_(logiikka)&veaction=edit&section=3" title="Muokkaa osiota Ominaisuudet" class="mw-editsection-visualeditor"><span>muokkaa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Konjunktio_(logiikka)&action=edit&section=3" title="Muokkaa osion lähdekoodia: Ominaisuudet"><span>muokkaa wikitekstiä</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Looginen konjunktio noudattaa laskulakeja, jotka pitkälti ovat analogisia esimerkiksi <a href="/wiki/Reaaliluku" title="Reaaliluku">reaalilukujen</a> laskusäännöille. Se on <a href="/wiki/Vaihdannaisuus" title="Vaihdannaisuus">vaihdannainen</a> ja <a href="/wiki/Liit%C3%A4nn%C3%A4isyys" title="Liitännäisyys">liitännäinen</a>, ja sille pätee myös <a href="/wiki/Osittelulaki" title="Osittelulaki">osittelulaki</a>, kun toisena laskutoimituksena on looginen <a href="/wiki/Disjunktio" title="Disjunktio">disjunktio</a>. Konjunktio on lisäksi <a href="/wiki/Idempotenssi" title="Idempotenssi">idempotentti</a> eli minkä tahansa lauseen konjunktiolla itsensä kanssa on sama totuusarvo kuin alkuperäisellä lauseella. Tätä havainnollistavat seuraavat kaaviot: </p> <ul><li><b>Vaihdannaisuus</b></li></ul> <table style="text-align: center; border: 1px solid darkgray;"> <tbody><tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\land B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>∧</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\land B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74954195333a8593163b93a9688695b8dc74da55" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.09ex; height:2.176ex;" alt="{\displaystyle A\land B}"></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Leftrightarrow }"></span>     </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B\land A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo>∧</mo> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B\land A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5920298dbda4592b71e53822ce01829cd77f4190" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.09ex; height:2.176ex;" alt="{\displaystyle B\land A}"></span> </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn0001.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Venn0001.svg/50px-Venn0001.svg.png" decoding="async" width="50" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Venn0001.svg/75px-Venn0001.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Venn0001.svg/100px-Venn0001.svg.png 2x" data-file-width="410" data-file-height="299" /></a></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Leftrightarrow }"></span>     </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn0001.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Venn0001.svg/50px-Venn0001.svg.png" decoding="async" width="50" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Venn0001.svg/75px-Venn0001.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Venn0001.svg/100px-Venn0001.svg.png 2x" data-file-width="410" data-file-height="299" /></a></span> </td></tr></tbody></table> <ul><li><b>Liitännäisyys</b></li></ul> <table style="text-align: center; border: 1px solid darkgray;"> <tbody><tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ~A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ~A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/17327d088840ce291c8db59b592489ef8e6e94bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:2.176ex;" alt="{\displaystyle ~A}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ~~~\land ~~~}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mo>∧</mo> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ~~~\land ~~~}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/296d4bd5f22dac2701fa42f57e9c5b65d1dd63f9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.066ex; height:2.009ex;" alt="{\displaystyle ~~~\land ~~~}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (B\land C)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>B</mi> <mo>∧</mo> <mi>C</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (B\land C)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78cc0188b905ef850ed33a9a4068e49794712b8d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.922ex; height:2.843ex;" alt="{\displaystyle (B\land C)}"></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Leftrightarrow }"></span>     </td> <td> </td> <td> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (A\land B)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>A</mi> <mo>∧</mo> <mi>B</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (A\land B)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebdcd2d1d13bc1f915aa141415965509a4e2b4f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.899ex; height:2.843ex;" alt="{\displaystyle (A\land B)}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ~~~\land ~~~}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mo>∧</mo> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ~~~\land ~~~}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/296d4bd5f22dac2701fa42f57e9c5b65d1dd63f9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.066ex; height:2.009ex;" alt="{\displaystyle ~~~\land ~~~}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ~C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ~C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35f52ed2496dc4077efa433abb4685684a158d7e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.347ex; height:2.176ex;" alt="{\displaystyle ~C}"></span> </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0101_0101.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Venn_0101_0101.svg/50px-Venn_0101_0101.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Venn_0101_0101.svg/75px-Venn_0101_0101.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/85/Venn_0101_0101.svg/100px-Venn_0101_0101.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ~~~\land ~~~}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mo>∧</mo> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ~~~\land ~~~}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/296d4bd5f22dac2701fa42f57e9c5b65d1dd63f9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.066ex; height:2.009ex;" alt="{\displaystyle ~~~\land ~~~}"></span> </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0000_0011.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Venn_0000_0011.svg/50px-Venn_0000_0011.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Venn_0000_0011.svg/75px-Venn_0000_0011.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Venn_0000_0011.svg/100px-Venn_0000_0011.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Leftrightarrow }"></span>     </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0000_0001.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Venn_0000_0001.svg/50px-Venn_0000_0001.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Venn_0000_0001.svg/75px-Venn_0000_0001.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Venn_0000_0001.svg/100px-Venn_0000_0001.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Leftrightarrow }"></span>     </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0001_0001.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Venn_0001_0001.svg/50px-Venn_0001_0001.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Venn_0001_0001.svg/75px-Venn_0001_0001.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Venn_0001_0001.svg/100px-Venn_0001_0001.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ~~~\land ~~~}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mo>∧</mo> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ~~~\land ~~~}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/296d4bd5f22dac2701fa42f57e9c5b65d1dd63f9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.066ex; height:2.009ex;" alt="{\displaystyle ~~~\land ~~~}"></span> </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0000_1111.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Venn_0000_1111.svg/50px-Venn_0000_1111.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Venn_0000_1111.svg/75px-Venn_0000_1111.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Venn_0000_1111.svg/100px-Venn_0000_1111.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td></tr></tbody></table> <ul><li><b>Osittelulaki loogisen disjunktion suhteen</b></li></ul> <table style="text-align: center; border: 1px solid darkgray;"> <tbody><tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ~A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ~A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/17327d088840ce291c8db59b592489ef8e6e94bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:2.176ex;" alt="{\displaystyle ~A}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \land }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \land }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6823e5a222eb3ca49672818ac3d13ec607052c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \land }"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (B\lor C)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>B</mi> <mo>∨</mo> <mi>C</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (B\lor C)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0c18aad468eb6ae0354f697dd4035fb970946d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.922ex; height:2.843ex;" alt="{\displaystyle (B\lor C)}"></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Leftrightarrow }"></span>     </td> <td> </td> <td> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (A\land B)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>A</mi> <mo>∧</mo> <mi>B</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (A\land B)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebdcd2d1d13bc1f915aa141415965509a4e2b4f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.899ex; height:2.843ex;" alt="{\displaystyle (A\land B)}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lor }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∨</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lor }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab47f6b1f589aedcf14638df1d63049d233d851a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \lor }"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (A\land C)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>A</mi> <mo>∧</mo> <mi>C</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (A\land C)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/887cc87745fae3b8e066d3d41dce3e430063844e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.901ex; height:2.843ex;" alt="{\displaystyle (A\land C)}"></span> </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0101_0101.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Venn_0101_0101.svg/50px-Venn_0101_0101.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Venn_0101_0101.svg/75px-Venn_0101_0101.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/85/Venn_0101_0101.svg/100px-Venn_0101_0101.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \land }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \land }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6823e5a222eb3ca49672818ac3d13ec607052c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \land }"></span> </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0011_1111.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/Venn_0011_1111.svg/50px-Venn_0011_1111.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/Venn_0011_1111.svg/75px-Venn_0011_1111.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/56/Venn_0011_1111.svg/100px-Venn_0011_1111.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Leftrightarrow }"></span>     </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0001_0101.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Venn_0001_0101.svg/50px-Venn_0001_0101.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Venn_0001_0101.svg/75px-Venn_0001_0101.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Venn_0001_0101.svg/100px-Venn_0001_0101.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Leftrightarrow }"></span>     </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0001_0001.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Venn_0001_0001.svg/50px-Venn_0001_0001.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Venn_0001_0001.svg/75px-Venn_0001_0001.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Venn_0001_0001.svg/100px-Venn_0001_0001.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lor }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∨</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lor }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab47f6b1f589aedcf14638df1d63049d233d851a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \lor }"></span> </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0000_0101.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Venn_0000_0101.svg/50px-Venn_0000_0101.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Venn_0000_0101.svg/75px-Venn_0000_0101.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Venn_0000_0101.svg/100px-Venn_0000_0101.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td></tr></tbody></table> <table class="collapsible collapsed" style="width: 100%; border: 1px solid #aaaaaa;"> <tbody><tr> <th bgcolor="#ccccff">muita </th></tr> <tr> <td> <p>liitännäisyys <a href="/w/index.php?title=Ekslusiivinen_disjunktio&action=edit&redlink=1" class="new" title="Ekslusiivinen disjunktio (sivua ei ole)">eksklusiivisen diskunktion</a> suhteen: </p> <table style="text-align: center; border: 1px solid darkgray;"> <tbody><tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ~A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ~A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/17327d088840ce291c8db59b592489ef8e6e94bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:2.176ex;" alt="{\displaystyle ~A}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \land }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \land }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6823e5a222eb3ca49672818ac3d13ec607052c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \land }"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (B\oplus C)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>B</mi> <mo>⊕</mo> <mi>C</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (B\oplus C)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f8d4800638f9d7524cd268e8e9443f12bf67afac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.18ex; height:2.843ex;" alt="{\displaystyle (B\oplus C)}"></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Leftrightarrow }"></span>     </td> <td> </td> <td> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (A\land B)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>A</mi> <mo>∧</mo> <mi>B</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (A\land B)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebdcd2d1d13bc1f915aa141415965509a4e2b4f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.899ex; height:2.843ex;" alt="{\displaystyle (A\land B)}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \oplus }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊕</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oplus }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b16e2bdaefee9eed86d866e6eba3ac47c710f60" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \oplus }"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (A\land C)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>A</mi> <mo>∧</mo> <mi>C</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (A\land C)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/887cc87745fae3b8e066d3d41dce3e430063844e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.901ex; height:2.843ex;" alt="{\displaystyle (A\land C)}"></span> </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0101_0101.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Venn_0101_0101.svg/50px-Venn_0101_0101.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Venn_0101_0101.svg/75px-Venn_0101_0101.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/85/Venn_0101_0101.svg/100px-Venn_0101_0101.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \land }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \land }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6823e5a222eb3ca49672818ac3d13ec607052c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \land }"></span> </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0011_1100.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Venn_0011_1100.svg/50px-Venn_0011_1100.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Venn_0011_1100.svg/75px-Venn_0011_1100.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Venn_0011_1100.svg/100px-Venn_0011_1100.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Leftrightarrow }"></span>     </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0001_0100.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Venn_0001_0100.svg/50px-Venn_0001_0100.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Venn_0001_0100.svg/75px-Venn_0001_0100.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Venn_0001_0100.svg/100px-Venn_0001_0100.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Leftrightarrow }"></span>     </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0001_0001.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Venn_0001_0001.svg/50px-Venn_0001_0001.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Venn_0001_0001.svg/75px-Venn_0001_0001.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Venn_0001_0001.svg/100px-Venn_0001_0001.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \oplus }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊕</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oplus }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b16e2bdaefee9eed86d866e6eba3ac47c710f60" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \oplus }"></span> </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0000_0101.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Venn_0000_0101.svg/50px-Venn_0000_0101.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Venn_0000_0101.svg/75px-Venn_0000_0101.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Venn_0000_0101.svg/100px-Venn_0000_0101.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td></tr></tbody></table> <p><br /> liitännäisyys materiaalisen <a href="/w/index.php?title=Nonimplikaatio&action=edit&redlink=1" class="new" title="Nonimplikaatio (sivua ei ole)">nonimplikaation</a> suhteen: </p> <table style="text-align: center; border: 1px solid darkgray;"> <tbody><tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ~A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ~A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/17327d088840ce291c8db59b592489ef8e6e94bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:2.176ex;" alt="{\displaystyle ~A}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \land }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \land }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6823e5a222eb3ca49672818ac3d13ec607052c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \land }"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (B\nrightarrow C)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>B</mi> <mo>↛</mo> <mi>C</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (B\nrightarrow C)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d881f71105d0587a2b95607cc353b2021b5b345" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.954ex; height:2.843ex;" alt="{\displaystyle (B\nrightarrow C)}"></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Leftrightarrow }"></span>     </td> <td> </td> <td> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (A\land B)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>A</mi> <mo>∧</mo> <mi>B</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (A\land B)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebdcd2d1d13bc1f915aa141415965509a4e2b4f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.899ex; height:2.843ex;" alt="{\displaystyle (A\land B)}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↛</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c458d67617e028ed10948d2dbcfef80e9e060a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \nrightarrow }"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (A\land C)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>A</mi> <mo>∧</mo> <mi>C</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (A\land C)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/887cc87745fae3b8e066d3d41dce3e430063844e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.901ex; height:2.843ex;" alt="{\displaystyle (A\land C)}"></span> </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0101_0101.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Venn_0101_0101.svg/50px-Venn_0101_0101.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Venn_0101_0101.svg/75px-Venn_0101_0101.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/85/Venn_0101_0101.svg/100px-Venn_0101_0101.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \land }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \land }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6823e5a222eb3ca49672818ac3d13ec607052c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \land }"></span> </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0011_0000.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Venn_0011_0000.svg/50px-Venn_0011_0000.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Venn_0011_0000.svg/75px-Venn_0011_0000.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Venn_0011_0000.svg/100px-Venn_0011_0000.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Leftrightarrow }"></span>     </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0001_0000.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Venn_0001_0000.svg/50px-Venn_0001_0000.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Venn_0001_0000.svg/75px-Venn_0001_0000.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Venn_0001_0000.svg/100px-Venn_0001_0000.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Leftrightarrow }"></span>     </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0001_0001.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Venn_0001_0001.svg/50px-Venn_0001_0001.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Venn_0001_0001.svg/75px-Venn_0001_0001.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Venn_0001_0001.svg/100px-Venn_0001_0001.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↛</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c458d67617e028ed10948d2dbcfef80e9e060a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \nrightarrow }"></span> </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0000_0101.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Venn_0000_0101.svg/50px-Venn_0000_0101.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Venn_0000_0101.svg/75px-Venn_0000_0101.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Venn_0000_0101.svg/100px-Venn_0000_0101.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td></tr></tbody></table> <p>liitännäisyys itsensä kanssa: </p> <table style="text-align: center; border: 1px solid darkgray;"> <tbody><tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ~A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ~A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/17327d088840ce291c8db59b592489ef8e6e94bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:2.176ex;" alt="{\displaystyle ~A}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \land }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \land }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6823e5a222eb3ca49672818ac3d13ec607052c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \land }"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (B\land C)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>B</mi> <mo>∧</mo> <mi>C</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (B\land C)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78cc0188b905ef850ed33a9a4068e49794712b8d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.922ex; height:2.843ex;" alt="{\displaystyle (B\land C)}"></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Leftrightarrow }"></span>     </td> <td> </td> <td> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (A\land B)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>A</mi> <mo>∧</mo> <mi>B</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (A\land B)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebdcd2d1d13bc1f915aa141415965509a4e2b4f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.899ex; height:2.843ex;" alt="{\displaystyle (A\land B)}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \land }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \land }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6823e5a222eb3ca49672818ac3d13ec607052c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \land }"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (A\land C)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>A</mi> <mo>∧</mo> <mi>C</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (A\land C)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/887cc87745fae3b8e066d3d41dce3e430063844e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.901ex; height:2.843ex;" alt="{\displaystyle (A\land C)}"></span> </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0101_0101.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Venn_0101_0101.svg/50px-Venn_0101_0101.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Venn_0101_0101.svg/75px-Venn_0101_0101.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/85/Venn_0101_0101.svg/100px-Venn_0101_0101.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \land }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \land }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6823e5a222eb3ca49672818ac3d13ec607052c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \land }"></span> </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0000_0011.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Venn_0000_0011.svg/50px-Venn_0000_0011.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Venn_0000_0011.svg/75px-Venn_0000_0011.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Venn_0000_0011.svg/100px-Venn_0000_0011.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Leftrightarrow }"></span>     </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0000_0001.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Venn_0000_0001.svg/50px-Venn_0000_0001.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Venn_0000_0001.svg/75px-Venn_0000_0001.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Venn_0000_0001.svg/100px-Venn_0000_0001.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Leftrightarrow }"></span>     </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0001_0001.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Venn_0001_0001.svg/50px-Venn_0001_0001.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Venn_0001_0001.svg/75px-Venn_0001_0001.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Venn_0001_0001.svg/100px-Venn_0001_0001.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \land }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \land }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6823e5a222eb3ca49672818ac3d13ec607052c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \land }"></span> </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0101_1111.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Venn_0101_1111.svg/50px-Venn_0101_1111.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Venn_0101_1111.svg/75px-Venn_0101_1111.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/25/Venn_0101_1111.svg/100px-Venn_0101_1111.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td></tr></tbody></table> </td></tr></tbody></table> <ul><li><b>Idempotenssi</b></li></ul> <table style="text-align: center; border: 1px solid darkgray;"> <tbody><tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ~A~}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>A</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ~A~}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00229fc56bafa7e9b522aedb3bed5dca455bc561" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.904ex; height:2.176ex;" alt="{\displaystyle ~A~}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ~\land ~}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mo>∧</mo> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ~\land ~}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b78b7e7950527f71b3b15b62d8459c636df43065" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.744ex; height:2.009ex;" alt="{\displaystyle ~\land ~}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ~A~}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>A</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ~A~}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00229fc56bafa7e9b522aedb3bed5dca455bc561" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.904ex; height:2.176ex;" alt="{\displaystyle ~A~}"></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Leftrightarrow }"></span>     </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A~}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A~}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5fc59051ffaf2eaace4f7b01f440b9067b722fb0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:2.176ex;" alt="{\displaystyle A~}"></span> </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn01.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Venn01.svg/36px-Venn01.svg.png" decoding="async" width="36" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Venn01.svg/54px-Venn01.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/06/Venn01.svg/72px-Venn01.svg.png 2x" data-file-width="280" data-file-height="280" /></a></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ~\land ~}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mo>∧</mo> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ~\land ~}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b78b7e7950527f71b3b15b62d8459c636df43065" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.744ex; height:2.009ex;" alt="{\displaystyle ~\land ~}"></span> </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn01.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Venn01.svg/36px-Venn01.svg.png" decoding="async" width="36" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Venn01.svg/54px-Venn01.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/06/Venn01.svg/72px-Venn01.svg.png 2x" data-file-width="280" data-file-height="280" /></a></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Leftrightarrow }"></span>     </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn01.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Venn01.svg/36px-Venn01.svg.png" decoding="async" width="36" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Venn01.svg/54px-Venn01.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/06/Venn01.svg/72px-Venn01.svg.png 2x" data-file-width="280" data-file-height="280" /></a></span> </td></tr></tbody></table> <ul><li><b><a href="/wiki/Monotoninen_funktio" title="Monotoninen funktio">Monotonisuus</a></b></li></ul> <table style="text-align: center; border: 1px solid darkgray;"> <tbody><tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\rightarrow B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo stretchy="false">→</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\rightarrow B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23efef033def56a67de7ded823f14626de26d174" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.121ex; height:2.176ex;" alt="{\displaystyle A\rightarrow B}"></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Rightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇒</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Rightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/469b737d167b9b28a74e27c7f5e35b5ea9256100" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Rightarrow }"></span>     </td> <td> </td> <td> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (A\land C)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>A</mi> <mo>∧</mo> <mi>C</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (A\land C)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/887cc87745fae3b8e066d3d41dce3e430063844e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.901ex; height:2.843ex;" alt="{\displaystyle (A\land C)}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">→</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53e574cc3aa5b4bf5f3f5906caf121a378eef08b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \rightarrow }"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (B\land C)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>B</mi> <mo>∧</mo> <mi>C</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (B\land C)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78cc0188b905ef850ed33a9a4068e49794712b8d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.922ex; height:2.843ex;" alt="{\displaystyle (B\land C)}"></span> </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_1011_1011.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/61/Venn_1011_1011.svg/50px-Venn_1011_1011.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/61/Venn_1011_1011.svg/75px-Venn_1011_1011.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/61/Venn_1011_1011.svg/100px-Venn_1011_1011.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Rightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇒</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Rightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/469b737d167b9b28a74e27c7f5e35b5ea9256100" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Rightarrow }"></span>     </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_1111_1011.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Venn_1111_1011.svg/50px-Venn_1111_1011.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Venn_1111_1011.svg/75px-Venn_1111_1011.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Venn_1111_1011.svg/100px-Venn_1111_1011.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Leftrightarrow }"></span>     </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0000_0101.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Venn_0000_0101.svg/50px-Venn_0000_0101.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Venn_0000_0101.svg/75px-Venn_0000_0101.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Venn_0000_0101.svg/100px-Venn_0000_0101.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">→</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53e574cc3aa5b4bf5f3f5906caf121a378eef08b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \rightarrow }"></span> </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn_0000_0011.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Venn_0000_0011.svg/50px-Venn_0000_0011.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Venn_0000_0011.svg/75px-Venn_0000_0011.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Venn_0000_0011.svg/100px-Venn_0000_0011.svg.png 2x" data-file-width="200" data-file-height="200" /></a></span> </td></tr></tbody></table> <ul><li><b>Totuuden säilyttävä validiteetti</b></li></ul> <p>Kun kaikki konjunktiolla yhdistettävät lauseet ovat tosia, konjunktio on tosi. </p> <table style="text-align: center; border: 1px solid darkgray;"> <tbody><tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\land B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>∧</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\land B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74954195333a8593163b93a9688695b8dc74da55" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.09ex; height:2.176ex;" alt="{\displaystyle A\land B}"></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Rightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇒</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Rightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/469b737d167b9b28a74e27c7f5e35b5ea9256100" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Rightarrow }"></span>     </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\lor B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>∨</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\lor B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b9c9c90857c12727201dd9e47a4e7c8658fdbc5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.09ex; height:2.176ex;" alt="{\displaystyle A\lor B}"></span> </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn0001.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Venn0001.svg/50px-Venn0001.svg.png" decoding="async" width="50" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Venn0001.svg/75px-Venn0001.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Venn0001.svg/100px-Venn0001.svg.png 2x" data-file-width="410" data-file-height="299" /></a></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Rightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇒</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Rightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/469b737d167b9b28a74e27c7f5e35b5ea9256100" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Rightarrow }"></span>     </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn0111.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Venn0111.svg/60px-Venn0111.svg.png" decoding="async" width="60" height="44" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Venn0111.svg/90px-Venn0111.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/30/Venn0111.svg/120px-Venn0111.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr> <tr> <td> </td> <td> </td> <td><small>(kokeiltava)</small> </td></tr></tbody></table> <ul><li><b>Epätotuuden säilyttävä validiteetti</b></li></ul> <p>Kun kaikki konjunktiolla yhdistettävät lauseet ovat epätosia, disjunktio on epätosi. </p> <table style="text-align: center; border: 1px solid darkgray;"> <tbody><tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\land B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>∧</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\land B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74954195333a8593163b93a9688695b8dc74da55" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.09ex; height:2.176ex;" alt="{\displaystyle A\land B}"></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Rightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇒</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Rightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/469b737d167b9b28a74e27c7f5e35b5ea9256100" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Rightarrow }"></span>     </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\land B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>∧</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\land B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74954195333a8593163b93a9688695b8dc74da55" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.09ex; height:2.176ex;" alt="{\displaystyle A\land B}"></span> </td></tr> <tr> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn0111.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Venn0111.svg/60px-Venn0111.svg.png" decoding="async" width="60" height="44" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Venn0111.svg/90px-Venn0111.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/30/Venn0111.svg/120px-Venn0111.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td> <td>    <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Rightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇒</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Rightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/469b737d167b9b28a74e27c7f5e35b5ea9256100" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Rightarrow }"></span>     </td> <td><span typeof="mw:File"><a href="/wiki/Tiedosto:Venn0111.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Venn0111.svg/50px-Venn0111.svg.png" decoding="async" width="50" height="37" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Venn0111.svg/75px-Venn0111.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/30/Venn0111.svg/100px-Venn0111.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr> <tr> <td><small>(kokeiltava)</small> </td> <td> </td> <td> </td></tr></tbody></table> <ul><li><b><a href="/w/index.php?title=Hadamardin_muunnos&action=edit&redlink=1" class="new" title="Hadamardin muunnos (sivua ei ole)">Walshin spektri</a>: (1, -1, 1, -1)</b></li></ul> <ul><li><b>Epälineaarisuus: 1</b> (funktio on <a href="/w/index.php?title=Taivutettu_funktio&action=edit&redlink=1" class="new" title="Taivutettu funktio (sivua ei ole)">taivutettu</a>)</li></ul> <p>Jos totuusarvoille käytetään <a href="/wiki/Bin%C3%A4%C3%A4riluku" class="mw-redirect" title="Binääriluku">binäärilukumerkintöjä</a> 1 (tosi) ja 0 (epätosi), looginen konjunktio toimii samoin kuin näiden lukujen normaali kertolasku. </p> <div class="mw-heading mw-heading2"><h2 id="Sovellukset_tietotekniikassa">Sovellukset tietotekniikassa</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Konjunktio_(logiikka)&veaction=edit&section=4" title="Muokkaa osiota Sovellukset tietotekniikassa" class="mw-editsection-visualeditor"><span>muokkaa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Konjunktio_(logiikka)&action=edit&section=4" title="Muokkaa osion lähdekoodia: Sovellukset tietotekniikassa"><span>muokkaa wikitekstiä</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Tiedosto:AND_Gate_diagram.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/AND_Gate_diagram.svg/150px-AND_Gate_diagram.svg.png" decoding="async" width="150" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/AND_Gate_diagram.svg/225px-AND_Gate_diagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/41/AND_Gate_diagram.svg/300px-AND_Gate_diagram.svg.png 2x" data-file-width="721" data-file-height="232" /></a><figcaption><a href="/wiki/AND-portti" title="AND-portti">AND-portti</a></figcaption></figure> <p>Useimmissa <a href="/wiki/Ohjelmointikieli" title="Ohjelmointikieli">ohjelmointikielissä</a> on konjunktiota vastaava operaattori. Se merkitään monissa ohjelmointikielissä <a href="/w/index.php?title=Varattu_sana&action=edit&redlink=1" class="new" title="Varattu sana (sivua ei ole)">varatulla sanalla</a> <code>and</code>, mutta esimerkiksi <a href="/wiki/C_(ohjelmointikieli)" title="C (ohjelmointikieli)">C:ssä</a> ja siihen pohjautuvissa ohjelmointikielissä kahdella <a href="/wiki/Et-merkki" class="mw-redirect" title="Et-merkki">et-merkillä</a> (<code>&&</code>). </p><p>Useimmissa ohjelmointikielissä looginen konjunktio antaa tulokseksi aina <a href="/w/index.php?title=Boolean&action=edit&redlink=1" class="new" title="Boolean (sivua ei ole)">boolean</a>-tyyppisen muuttujan, jolla on vain kaksi mahdollista arvoa: tosi (1) tai epätosi (0). Monissa <a href="/wiki/Vahva_tyypitys" class="mw-redirect" title="Vahva tyypitys">vahvasti tyypitetyissä</a> kielissä konjunktio voidaan sitä paitsi suorittaa vain, jos molemmat sillä yhdistettävät <a href="/wiki/Operandi" title="Operandi">operanditkin</a> ovat boolean-tyyppisiä. Joissakin heikosti tyypitetyissä kielissä, esimerkiksi <a href="/wiki/C_(ohjelmointikieli)" title="C (ohjelmointikieli)">C:ssä</a>, konjunktio voidaan kuitenkin suorittaa silloinkin, kun operandit ovat esimerkiksi kokonais- tai reaalilukutyyppisiä; tällöin tuloksena on 0 (epätosi), jos ainakin jompikumpi operandi on nolla, mulloin tuloksena on 1 (tosi). Tällöin siis operandien kaikkien muiden arvon kuin nollan katsotaan vastaavan totuusarvoa tosi. </p><p>Konjunktiota vastaava <a href="/wiki/Looginen_portti" title="Looginen portti">looginen portti</a> on <a href="/wiki/AND-portti" title="AND-portti">AND-portti</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Biteittäinen_operaatio"><span id="Biteitt.C3.A4inen_operaatio"></span>Biteittäinen operaatio</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Konjunktio_(logiikka)&veaction=edit&section=5" title="Muokkaa osiota Biteittäinen operaatio" class="mw-editsection-visualeditor"><span>muokkaa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Konjunktio_(logiikka)&action=edit&section=5" title="Muokkaa osion lähdekoodia: Biteittäinen operaatio"><span>muokkaa wikitekstiä</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Joissakin ohjelmointikielissä on määritelty myös <i>biteittäinen konjunktio'</i>. Tällöin operandit, jotka voivat olla esimerkiksi <a href="/wiki/Bin%C3%A4%C3%A4riluku" class="mw-redirect" title="Binääriluku">binäärisiä</a> <a href="/wiki/Kokonaisluku" title="Kokonaisluku">kokonaislukuja</a>, käydään läpi bitti bitiltä ja suoritetaan konjunktio-operaatiot kummankin operandin vastaavien bittien välillä. Tuloksena saadaan muuttuja, jossa kunkin bitin arvo riippuu operandien bittien arvoista seuraavasti: </p> <ul><li>0 <code>and</code> 0 = 0</li> <li>0 <code>and</code> 1 = 0</li> <li>1 <code>and</code> 0 = 0</li> <li>1 <code>and</code> 1 = 1</li></ul> <p>Käymällä bitit läpi esimerkiksi binääriluvuista 11001010 ja 10100011 saadaan tulokseksi 10000010. </p><p>Biteittäinen konjunktio on käytettävissä muun muassa <a href="/wiki/C_(ohjelmointikieli)" title="C (ohjelmointikieli)">C-kielessä</a>, jossa se merkitään yhdellä et-merkillä (<code>&</code>). </p><p>Biteittäisellä konjunktiolla voidaan muun muassa selvittää, minkä annetussa bittijonossa on jonkin tietyn bitin arvo. Esimerkiksi laskutoimitus <code>10011101 AND 00001000</code> antaa tulokseksi bittijonon 00001000, joka osoittaa, että vasemmanpuoleisen luvun viidennen bitin arvo on 1. </p> <div class="mw-heading mw-heading2"><h2 id="Leikkaus">Leikkaus</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Konjunktio_(logiikka)&veaction=edit&section=6" title="Muokkaa osiota Leikkaus" class="mw-editsection-visualeditor"><span>muokkaa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Konjunktio_(logiikka)&action=edit&section=6" title="Muokkaa osion lähdekoodia: Leikkaus"><span>muokkaa wikitekstiä</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Konjunktiota vastaava operaatio <a href="/wiki/Joukko-oppi" title="Joukko-oppi">joukko-opissa</a> on <a href="/wiki/Leikkaus_(matematiikka)" title="Leikkaus (matematiikka)">leikkaus</a>. Kahden joukon leikkaus määritelläänkin konjunktion avulla: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a\in A\cap B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>∈</mo> <mi>A</mi> <mo>∩</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\in A\cap B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/34db77e79a0b73a2a10c23539c78c50966fdc28a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.16ex; height:2.176ex;" alt="{\displaystyle a\in A\cap B}"></span>, jos ja vain jos <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a\in A\land a\in B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>∈</mo> <mi>A</mi> <mo>∧</mo> <mi>a</mi> <mo>∈</mo> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\in A\land a\in B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c6a3ec79cade57b2f48ae360377ba9ea62296838" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:14.231ex; height:2.176ex;" alt="{\displaystyle a\in A\land a\in B}"></span>. Toisin sanoen alkio <i>a</i> kuuluu joukkojen <i>A</i> ja <i>B</i> leikkaukseen, jos ja vain jos se kuuluu molempiin näistä joukoista, Tämän vuoksi joukko-opillinen leikkaus noudattaa pitkälti samoja sääntöjä kuin konjunktiokin: sillekin pätevät vaihdanta-, liitäntä-, osittelu- ja <a href="/wiki/De_Morganin_lait" title="De Morganin lait">de Morganin lait</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Luonnolliset_kielet">Luonnolliset kielet</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Konjunktio_(logiikka)&veaction=edit&section=7" title="Muokkaa osiota Luonnolliset kielet" class="mw-editsection-visualeditor"><span>muokkaa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Konjunktio_(logiikka)&action=edit&section=7" title="Muokkaa osion lähdekoodia: Luonnolliset kielet"><span>muokkaa wikitekstiä</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Matemaattinen_logiikka" title="Matemaattinen logiikka">Matemaattisessa logiikassa</a> määritellyt käsitteet ovat merkitykseltään erilaisia kuin luonnollisen kielen sanat yleensä ovat. Suomen kielessä loogista konjunktiota vastaa lähinnä sana <a href="/wiki/Konjunktio_(kielitiede)" title="Konjunktio (kielitiede)">kieliopillinen konjunktio</a> <i>ja</i>. Tätä sanaa, samoin kuin sen vastineita useissa muissakin kielissä, käytetään kuitenkin myös tavoilla, jotka eivät vastaa loogisen konjunktion käsitettä. Toisinaan sillä ilmaistaan seurausta tai uhkausta, esimerkiksi: "vielä yksi sana, ja minä lähden", jonkin asian jatkamista huomattavan kauan, esimerkiksi "miettii ja miettii", tai sitä käytetään yhdistämään jonkin luvun tai määrän pienempää yksikköä suurempaan, esimerkiksi "kello 12 ja 50" (=12.50) tai <a href="/wiki/Tuhannen_ja_yhden_y%C3%B6n_tarinat" class="mw-redirect" title="Tuhannen ja yhden yön tarinat">Tuhannen ja yhden yön tarinat</a>.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Katso_myös"><span id="Katso_my.C3.B6s"></span>Katso myös</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Konjunktio_(logiikka)&veaction=edit&section=8" title="Muokkaa osiota Katso myös" class="mw-editsection-visualeditor"><span>muokkaa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Konjunktio_(logiikka)&action=edit&section=8" title="Muokkaa osion lähdekoodia: Katso myös"><span>muokkaa wikitekstiä</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Disjunktio" title="Disjunktio">Disjunktio</a></li> <li><a href="/wiki/AND-portti" title="AND-portti">AND-portti</a></li> <li><a href="/wiki/Propositiologiikka" title="Propositiologiikka">Propositiologiikka</a></li> <li><a href="/wiki/Boolen_algebra" title="Boolen algebra">Boolen algebra</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Lähteet"><span id="L.C3.A4hteet"></span>Lähteet</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Konjunktio_(logiikka)&veaction=edit&section=9" title="Muokkaa osiota Lähteet" class="mw-editsection-visualeditor"><span>muokkaa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Konjunktio_(logiikka)&action=edit&section=9" title="Muokkaa osion lähdekoodia: Lähteet"><span>muokkaa wikitekstiä</span></a><span class="mw-editsection-bracket">]</span></span></div> <div id="viitteet-malline" class="viitteet-malline" style="list-style-type:decimal;"><ol class="references"> <li id="cite_note-Hazewinkel-1"><span class="mw-cite-backlink">↑ <a href="#cite_ref-Hazewinkel_1-0"><sup><i>a</i></sup></a> <a href="#cite_ref-Hazewinkel_1-1"><sup><i>b</i></sup></a></span> <span class="reference-text"><span class="kirjaviite" title="Kirjaviite">”Conjunction”, <i>Encyclopedia of Mathematics</i>.  Springer, The European Mathematical Society.  <a href="/wiki/Toiminnot:Kirjal%C3%A4hteet/978-1-55608-010-4" title="Toiminnot:Kirjalähteet/978-1-55608-010-4">ISBN 978-1-55608-010-4</a>  <a rel="nofollow" class="external text" href="http://www.encyclopediaofmath.org/index.php/Conjunction">Teoksen verkkoversio</a>.</span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><span class="kirjaviite" title="Kirjaviite">Jósef Maria Bochenski: <i>A Précis of Mathematical Logic</i>.  (Otto Bird kääntänyt englanniksi ranskalaiista ja saksalaisista laitoksista)  Dordrecht:  D. Reidel, 1959. </span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><span class="kirjaviite" title="Kirjaviite">”Ja”, <i>Nykysuomen sanakirja, 1. osa (A-K), 11. painos</i>, s. 697.  Suomalaisen kirjallisuuden seura, WSOY, 1989.  <a href="/wiki/Toiminnot:Kirjal%C3%A4hteet/951-0-09105-7" title="Toiminnot:Kirjalähteet/951-0-09105-7">ISBN 951-0-09105-7</a> </span></span> </li> </ol> </div> <div class="mw-heading mw-heading2"><h2 id="Aiheesta_muualla">Aiheesta muualla</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Konjunktio_(logiikka)&veaction=edit&section=10" title="Muokkaa osiota Aiheesta muualla" class="mw-editsection-visualeditor"><span>muokkaa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Konjunktio_(logiikka)&action=edit&section=10" title="Muokkaa osion lähdekoodia: Aiheesta muualla"><span>muokkaa wikitekstiä</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="verkkoviite" title="Verkkoviite"><a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/conjunction.html">Conjunction</a> MathWorld. 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data-language-autonym="Čeština" data-language-local-name="tšekki" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Konjunktion_(logik)" title="Konjunktion (logik) — tanska" lang="da" hreflang="da" data-title="Konjunktion (logik)" data-language-autonym="Dansk" data-language-local-name="tanska" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Konjunktion_(Logik)" title="Konjunktion (Logik) — saksa" lang="de" hreflang="de" data-title="Konjunktion (Logik)" data-language-autonym="Deutsch" data-language-local-name="saksa" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Konjunktsioon" title="Konjunktsioon — viro" lang="et" hreflang="et" data-title="Konjunktsioon" data-language-autonym="Eesti" data-language-local-name="viro" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9B%CE%BF%CE%B3%CE%B9%CE%BA%CE%AE_%CF%83%CF%8D%CE%B6%CE%B5%CF%85%CE%BE%CE%B7" title="Λογική σύζευξη — kreikka" lang="el" hreflang="el" data-title="Λογική σύζευξη" data-language-autonym="Ελληνικά" data-language-local-name="kreikka" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://eml.wikipedia.org/wiki/Congiunsi%C3%B2un_l%C3%B2gica" title="Congiunsiòun lògica — Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Congiunsiòun lògica" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target"><span>Emiliàn e rumagnòl</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Logical_conjunction" title="Logical conjunction — englanti" lang="en" hreflang="en" data-title="Logical conjunction" data-language-autonym="English" data-language-local-name="englanti" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Conjunci%C3%B3n_l%C3%B3gica" title="Conjunción lógica — espanja" lang="es" hreflang="es" data-title="Conjunción lógica" data-language-autonym="Español" data-language-local-name="espanja" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Konjunkcio_(logiko)" title="Konjunkcio (logiko) — esperanto" lang="eo" hreflang="eo" data-title="Konjunkcio (logiko)" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Konjuntzio_logiko" title="Konjuntzio logiko — baski" lang="eu" hreflang="eu" data-title="Konjuntzio logiko" data-language-autonym="Euskara" data-language-local-name="baski" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B9%D8%B7%D9%81_%D9%85%D9%86%D8%B7%D9%82%DB%8C" title="عطف منطقی — persia" lang="fa" hreflang="fa" data-title="عطف منطقی" data-language-autonym="فارسی" data-language-local-name="persia" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Conjonction_logique" title="Conjonction logique — ranska" lang="fr" hreflang="fr" data-title="Conjonction logique" data-language-autonym="Français" data-language-local-name="ranska" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%85%BC%EB%A6%AC%EA%B3%B1" title="논리곱 — korea" lang="ko" hreflang="ko" data-title="논리곱" data-language-autonym="한국어" data-language-local-name="korea" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BF%D5%B8%D5%B6%D5%B5%D5%B8%D6%82%D5%B6%D5%AF%D6%81%D5%AB%D5%A1" title="Կոնյունկցիա — armenia" lang="hy" hreflang="hy" data-title="Կոնյունկցիա" data-language-autonym="Հայերեն" data-language-local-name="armenia" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Congiunzione_logica" title="Congiunzione logica — italia" lang="it" hreflang="it" data-title="Congiunzione logica" data-language-autonym="Italiano" data-language-local-name="italia" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%95%D7%92%D7%9D_(%D7%9C%D7%95%D7%92%D7%99%D7%A7%D7%94)" title="וגם (לוגיקה) — heprea" lang="he" hreflang="he" data-title="וגם (לוגיקה)" data-language-autonym="עברית" data-language-local-name="heprea" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%8A%D1%8E%D0%BD%D0%BA%D1%86%D0%B8%D1%8F" title="Конъюнкция — kazakki" lang="kk" hreflang="kk" data-title="Конъюнкция" data-language-autonym="Қазақша" data-language-local-name="kazakki" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%8A%D1%8E%D0%BD%D0%BA%D1%86%D0%B8%D1%8F" title="Конъюнкция — kirgiisi" lang="ky" hreflang="ky" data-title="Конъюнкция" data-language-autonym="Кыргызча" data-language-local-name="kirgiisi" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Konjunkcija_(logika)" title="Konjunkcija (logika) — liettua" lang="lt" hreflang="lt" data-title="Konjunkcija (logika)" data-language-autonym="Lietuvių" data-language-local-name="liettua" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Dobi" title="Dobi — lombardi" lang="lmo" hreflang="lmo" data-title="Dobi" data-language-autonym="Lombard" data-language-local-name="lombardi" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Konjunkci%C3%B3_(logika)" title="Konjunkció (logika) — unkari" lang="hu" hreflang="hu" data-title="Konjunkció (logika)" data-language-autonym="Magyar" data-language-local-name="unkari" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B8%D1%87%D0%BA%D0%B0_%D0%BA%D0%BE%D0%BD%D1%98%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" title="Логичка конјункција — makedonia" lang="mk" hreflang="mk" data-title="Логичка конјункција" data-language-autonym="Македонски" data-language-local-name="makedonia" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Logische_conjunctie" title="Logische conjunctie — hollanti" lang="nl" hreflang="nl" data-title="Logische conjunctie" data-language-autonym="Nederlands" data-language-local-name="hollanti" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E8%AB%96%E7%90%86%E7%A9%8D" title="論理積 — japani" lang="ja" hreflang="ja" data-title="論理積" data-language-autonym="日本語" data-language-local-name="japani" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Konjunksjon_(logikk)" title="Konjunksjon (logikk) — norjan bokmål" lang="nb" hreflang="nb" data-title="Konjunksjon (logikk)" data-language-autonym="Norsk bokmål" data-language-local-name="norjan bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Congionsion" title="Congionsion — piemonte" lang="pms" hreflang="pms" data-title="Congionsion" data-language-autonym="Piemontèis" data-language-local-name="piemonte" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Koniunkcja_(logika)" title="Koniunkcja (logika) — puola" lang="pl" hreflang="pl" data-title="Koniunkcja (logika)" data-language-autonym="Polski" data-language-local-name="puola" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Conjun%C3%A7%C3%A3o_l%C3%B3gica" title="Conjunção lógica — portugali" lang="pt" hreflang="pt" data-title="Conjunção lógica" data-language-autonym="Português" data-language-local-name="portugali" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%8A%D1%8E%D0%BD%D0%BA%D1%86%D0%B8%D1%8F" title="Конъюнкция — venäjä" lang="ru" hreflang="ru" data-title="Конъюнкция" data-language-autonym="Русский" data-language-local-name="venäjä" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Konjuksioni" title="Konjuksioni — albania" lang="sq" hreflang="sq" data-title="Konjuksioni" data-language-autonym="Shqip" data-language-local-name="albania" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Logical_conjunction" title="Logical conjunction — Simple English" lang="en-simple" hreflang="en-simple" data-title="Logical conjunction" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Konjunkcia_(logika)" title="Konjunkcia (logika) — slovakki" lang="sk" hreflang="sk" data-title="Konjunkcia (logika)" data-language-autonym="Slovenčina" data-language-local-name="slovakki" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Konjunkcija_(logika)" title="Konjunkcija (logika) — sloveeni" lang="sl" hreflang="sl" data-title="Konjunkcija (logika)" data-language-autonym="Slovenščina" data-language-local-name="sloveeni" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B8%D1%87%D0%BA%D0%B0_%D0%BA%D0%BE%D0%BD%D1%98%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" title="Логичка конјункција — serbia" lang="sr" hreflang="sr" data-title="Логичка конјункција" data-language-autonym="Српски / srpski" data-language-local-name="serbia" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Logi%C4%8Dka_konjunkcija" title="Logička konjunkcija — serbokroaatti" lang="sh" hreflang="sh" data-title="Logička konjunkcija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbokroaatti" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Konjunktion_(logik)" title="Konjunktion (logik) — ruotsi" lang="sv" hreflang="sv" data-title="Konjunktion (logik)" data-language-autonym="Svenska" data-language-local-name="ruotsi" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B9%80%E0%B8%8A%E0%B8%B7%E0%B9%88%E0%B8%AD%E0%B8%A1%E0%B9%80%E0%B8%8A%E0%B8%B4%E0%B8%87%E0%B8%95%E0%B8%A3%E0%B8%A3%E0%B8%81%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C" title="การเชื่อมเชิงตรรกศาสตร์ — thai" lang="th" hreflang="th" data-title="การเชื่อมเชิงตรรกศาสตร์" data-language-autonym="ไทย" data-language-local-name="thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%27%D1%8E%D0%BD%D0%BA%D1%86%D1%96%D1%8F" title="Кон'юнкція — ukraina" lang="uk" hreflang="uk" data-title="Кон'юнкція" data-language-autonym="Українська" data-language-local-name="ukraina" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%82%8F%E8%BC%AF%E8%88%87" title="邏輯與 — kantoninkiina" lang="yue" hreflang="yue" data-title="邏輯與" data-language-autonym="粵語" data-language-local-name="kantoninkiina" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%80%BB%E8%BE%91%E4%B8%8E" title="逻辑与 — kiina" lang="zh" hreflang="zh" data-title="逻辑与" data-language-autonym="中文" data-language-local-name="kiina" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q191081#sitelinks-wikipedia" title="Muokkaa kieltenvälisiä linkkejä" class="wbc-editpage">Muokkaa linkkejä</a></span></div> </div> </nav> </div> </div> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Sivua on viimeksi muutettu 12. marraskuuta 2024 kello 21.10.</li> <li id="footer-info-copyright">Teksti on saatavilla <a 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