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Available in 23 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-23" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">23 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8B%99%E1%88%AD_%E1%8C%8D%E1%88%8D%E1%89%A3%E1%8C%AD" title="ዙር ግልባጭ – Amharic" lang="am" hreflang="am" data-title="ዙር ግልባጭ" data-language-autonym="አማርኛ" data-language-local-name="Amharic" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B9%D9%83%D8%B3_%D9%86%D9%82%D9%8A%D8%B6" title="عكس نقيض – Arabic" lang="ar" hreflang="ar" data-title="عكس نقيض" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Contraposici%C3%B3_l%C3%B2gica" title="Contraposició lògica – Catalan" lang="ca" hreflang="ca" data-title="Contraposició lògica" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Kontraposition" title="Kontraposition – Danish" lang="da" hreflang="da" data-title="Kontraposition" data-language-autonym="Dansk" data-language-local-name="Danish" 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/Kontraposition" title="Kontraposition – German" lang="de" hreflang="de" data-title="Kontraposition" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Contraposition" title="Contraposition – English" lang="en" hreflang="en" data-title="Contraposition" data-language-autonym="English" data-language-local-name="English" 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/Contraposici%C3%B3n_l%C3%B3gica" title="Contraposición lógica – Spanish" lang="es" hreflang="es" data-title="Contraposición lógica" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B9%DA%A9%D8%B3_%D9%86%D9%82%DB%8C%D8%B6" title="عکس نقیض – Persian" lang="fa" hreflang="fa" data-title="عکس نقیض" data-language-autonym="فارسی" data-language-local-name="Persian" 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/Proposition_contrapos%C3%A9e" title="Proposition contraposée – French" lang="fr" hreflang="fr" data-title="Proposition contraposée" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Contraposici%C3%B3n" title="Contraposición – Galician" lang="gl" hreflang="gl" data-title="Contraposición" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%8C%80%EC%9A%B0_(%EB%85%BC%EB%A6%AC%ED%95%99)" title="대우 (논리학) – Korean" lang="ko" hreflang="ko" data-title="대우 (논리학)" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Contraposition" title="Contraposition – Interlingua" lang="ia" hreflang="ia" data-title="Contraposition" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Contrapposizione" title="Contrapposizione – Italian" lang="it" hreflang="it" data-title="Contrapposizione" data-language-autonym="Italiano" data-language-local-name="Italian" 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%A7%D7%95%D7%A0%D7%98%D7%A8%D7%94_%D7%A4%D7%95%D7%96%D7%99%D7%98%D7%99%D7%91" title="קונטרה פוזיטיב – Hebrew" lang="he" hreflang="he" data-title="קונטרה פוזיטיב" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Bewijs_door_contrapositie" title="Bewijs door contrapositie – Dutch" lang="nl" hreflang="nl" data-title="Bewijs door contrapositie" data-language-autonym="Nederlands" data-language-local-name="Dutch" 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/%E5%AF%BE%E5%81%B6_(%E8%AB%96%E7%90%86%E5%AD%A6)" 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href="https://ru.wikipedia.org/wiki/%D0%97%D0%B0%D0%BA%D0%BE%D0%BD_%D0%BA%D0%BE%D0%BD%D1%82%D1%80%D0%B0%D0%BF%D0%BE%D0%B7%D0%B8%D1%86%D0%B8%D0%B8" title="Закон контрапозиции – Russian" lang="ru" hreflang="ru" data-title="Закон контрапозиции" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BD%D1%82%D1%80%D0%B0%D0%BF%D0%BE%D0%B7%D0%B8%D1%86%D0%B8%D1%98%D0%B0" title="Контрапозиција – Serbian" lang="sr" hreflang="sr" data-title="Контрапозиција" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Kontraposition" title="Kontraposition – Swedish" lang="sv" hreflang="sv" data-title="Kontraposition" 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class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Simple English Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p>In <a href="/wiki/Logic" title="Logic">logic</a> and <a href="/wiki/Mathematics" title="Mathematics">math</a>, contraposition is the right way to reverse "if-then" statements. For example, the contrapositive of the sentence <i>"If it is raining, then I wear my coat"</i> is the sentence <i>"If I don't wear my coat, then it isn't raining."</i> If the original sentence is correct, the contrapositive is always correct. </p><p>It is easier to see how contraposition is the right way to reverse an if-then statement by looking at two other reversals that can sometimes look similar, but are bad logic: </p><p><b>Inversion</b> </p><p><i>"If it is not raining, then I don't wear my coat."</i> This is wrong as one can wear a coat for other reasons (eg. It is snowing). In this statement, we have made both the "if" and the "then" statements negative. </p><p><b>Conversion</b> </p><p><i>"If I wear my coat, then it is raining."</i> This is wrong as wearing a coat doesn't cause it to rain. In this statement we have switched the "if" and "then" statements. </p><p>In technical writing: the contrapositive of <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 P\rightarrow Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo stretchy="false">→</mo> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P\rightarrow Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86439ea857adc8eaec93c4d14270b8ba6bd2a6a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.198ex; height:2.509ex;" alt="{\displaystyle P\rightarrow Q}"></span> is <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 Q\rightarrow \neg P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">¬</mi> <mi>Q</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">¬</mi> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \neg Q\rightarrow \neg P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2cda72a5ed034bbb1cdedb9b3c740e0900579a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.298ex; height:2.509ex;" alt="{\displaystyle \neg Q\rightarrow \neg P}"></span>. The "<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>" means "if-then" (If P then Q), and the "<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 P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">¬</mi> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \neg P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5eb0d6c8752f8c7256d69c62e77dfe4c466dbe58" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.296ex; height:2.176ex;" alt="{\displaystyle \neg P}"></span>" means "not P" (eg. "it is not raining"). </p>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://simple.wikipedia.org/w/index.php?title=Contraposition&oldid=7457669">https://simple.wikipedia.org/w/index.php?title=Contraposition&oldid=7457669</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Special:Categories" title="Special:Categories">Categories</a>: <ul><li><a href="/wiki/Category:Logic" title="Category:Logic">Logic</a></li><li><a href="/wiki/Category:Mathematics" title="Category:Mathematics">Mathematics</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last changed on 3 April 2021, at 01:27.</li> <li id="footer-info-copyright">Text is available under the <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike License</a> and the <a href="/wiki/Wikipedia:Text_of_the_GNU_Free_Documentation_License" title="Wikipedia:Text of the GNU Free Documentation License">GFDL</a>; additional terms may apply. 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