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mw-first-heading"><span class="mw-page-title-main">Dan en slechts dan als</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Ga naar een artikel in een andere taal. Beschikbaar in 49 talen" > <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-49" 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">49 talen</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A5%D8%B0%D8%A7_%D9%88%D9%81%D9%82%D8%B7_%D8%A5%D8%B0%D8%A7" title="إذا وفقط إذا – Arabisch" lang="ar" hreflang="ar" data-title="إذا وفقط إذا" data-language-autonym="العربية" data-language-local-name="Arabisch" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A2%D0%BE%D0%B3%D0%B0%D0%B2%D0%B0_%D0%B8_%D1%81%D0%B0%D0%BC%D0%BE_%D1%82%D0%BE%D0%B3%D0%B0%D0%B2%D0%B0,_%D0%BA%D0%BE%D0%B3%D0%B0%D1%82%D0%BE" title="Тогава и само тогава, когато – Bulgaars" lang="bg" hreflang="bg" data-title="Тогава и само тогава, когато" data-language-autonym="Български" data-language-local-name="Bulgaars" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Si_i_nom%C3%A9s_si" title="Si i només si – Catalaans" lang="ca" hreflang="ca" data-title="Si i només si" data-language-autonym="Català" data-language-local-name="Catalaans" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%C3%87%D0%B0%D0%B2%C4%83%D0%BD_%D1%87%D1%83%D1%85%D0%BD%D0%B5_%D1%82%D0%B0%D1%82%D0%B0_%C3%A7%D0%B0%D0%B2%C4%83%D0%BD_%D1%87%D1%83%D1%85%D0%BD%D0%B5_%C3%A7%D0%B5%C3%A7" title="Çавăн чухне тата çавăн чухне çеç – Tsjoevasjisch" lang="cv" hreflang="cv" data-title="Çавăн чухне тата çавăн чухне çеç" data-language-autonym="Чӑвашла" data-language-local-name="Tsjoevasjisch" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Os_ac_yn_unig_os" title="Os ac yn unig os – Welsh" lang="cy" hreflang="cy" data-title="Os ac yn unig os" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Biimplikation" title="Biimplikation – Deens" lang="da" hreflang="da" data-title="Biimplikation" data-language-autonym="Dansk" data-language-local-name="Deens" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Genau_dann,_wenn" title="Genau dann, wenn – Duits" lang="de" hreflang="de" data-title="Genau dann, wenn" data-language-autonym="Deutsch" data-language-local-name="Duits" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CE%BD_%CE%BA%CE%B1%CE%B9_%CE%BC%CF%8C%CE%BD%CE%BF_%CE%B1%CE%BD" title="Αν και μόνο αν – Grieks" lang="el" hreflang="el" data-title="Αν και μόνο αν" data-language-autonym="Ελληνικά" data-language-local-name="Grieks" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/If_and_only_if" title="If and only if – Engels" lang="en" hreflang="en" data-title="If and only if" data-language-autonym="English" data-language-local-name="Engels" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Se_kaj_nur_se" title="Se kaj nur se – Esperanto" lang="eo" hreflang="eo" data-title="Se kaj nur se" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Bicondicional" title="Bicondicional – Spaans" lang="es" hreflang="es" data-title="Bicondicional" data-language-autonym="Español" data-language-local-name="Spaans" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Parajasti_siis,_kui" title="Parajasti siis, kui – Estisch" lang="et" hreflang="et" data-title="Parajasti siis, kui" data-language-autonym="Eesti" data-language-local-name="Estisch" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Inplikazio_bikoitz" title="Inplikazio bikoitz – Baskisch" lang="eu" hreflang="eu" data-title="Inplikazio bikoitz" data-language-autonym="Euskara" data-language-local-name="Baskisch" 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%A7%DA%AF%D8%B1_%D9%88_%D8%AA%D9%86%D9%87%D8%A7_%D8%A7%DA%AF%D8%B1" title="اگر و تنها اگر – Perzisch" lang="fa" hreflang="fa" data-title="اگر و تنها اگر" data-language-autonym="فارسی" data-language-local-name="Perzisch" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Jos_ja_vain_jos" title="Jos ja vain jos – Fins" lang="fi" hreflang="fi" data-title="Jos ja vain jos" data-language-autonym="Suomi" data-language-local-name="Fins" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Se_e_s%C3%B3_se" title="Se e só se – Galicisch" lang="gl" hreflang="gl" data-title="Se e só se" data-language-autonym="Galego" data-language-local-name="Galicisch" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%9D_%D7%95%D7%A8%D7%A7_%D7%90%D7%9D" title="אם ורק אם – Hebreeuws" lang="he" hreflang="he" data-title="אם ורק אם" data-language-autonym="עברית" data-language-local-name="Hebreeuws" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AF%E0%A4%A6%E0%A4%BF_%E0%A4%94%E0%A4%B0_%E0%A4%95%E0%A5%87%E0%A4%B5%E0%A4%B2_%E0%A4%AF%E0%A4%A6%E0%A4%BF" title="यदि और केवल यदि – Hindi" lang="hi" hreflang="hi" data-title="यदि और केवल यदि" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Akko" title="Akko – Kroatisch" lang="hr" hreflang="hr" data-title="Akko" data-language-autonym="Hrvatski" data-language-local-name="Kroatisch" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Bikondicion%C3%A1lis" title="Bikondicionális – Hongaars" lang="hu" hreflang="hu" data-title="Bikondicionális" data-language-autonym="Magyar" data-language-local-name="Hongaars" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Si_e_solmente_si" title="Si e solmente si – Interlingua" lang="ia" hreflang="ia" data-title="Si e solmente si" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Jika_dan_hanya_jika" title="Jika dan hanya jika – Indonesisch" lang="id" hreflang="id" data-title="Jika dan hanya jika" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesisch" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Se_e_nur_se" title="Se e nur se – Ido" lang="io" hreflang="io" data-title="Se e nur se" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Eff" title="Eff – IJslands" lang="is" hreflang="is" data-title="Eff" data-language-autonym="Íslenska" data-language-local-name="IJslands" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Se_e_solo_se" title="Se e solo se – Italiaans" lang="it" hreflang="it" data-title="Se e solo se" data-language-autonym="Italiano" data-language-local-name="Italiaans" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%90%8C%E5%80%A4" title="同値 – Japans" lang="ja" hreflang="ja" data-title="同値" data-language-autonym="日本語" data-language-local-name="Japans" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%95%D0%B3%D0%B5%D1%80_%D1%82%D0%B5%D0%BA_%D0%B5%D0%B3%D0%B5%D1%80" title="Егер тек егер – Kazachs" lang="kk" hreflang="kk" data-title="Егер тек егер" data-language-autonym="Қазақша" data-language-local-name="Kazachs" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Se_e_dom%C3%A0_se" title="Se e domà se – Lombardisch" lang="lmo" hreflang="lmo" data-title="Se e domà se" data-language-autonym="Lombard" data-language-local-name="Lombardisch" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Tada_ir_tik_tada_(teiginys)" title="Tada ir tik tada (teiginys) – Litouws" lang="lt" hreflang="lt" data-title="Tada ir tik tada (teiginys)" data-language-autonym="Lietuvių" data-language-local-name="Litouws" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%90%D0%BA%D0%BE_%D0%B8_%D1%81%D0%B0%D0%BC%D0%BE_%D0%B0%D0%BA%D0%BE" title="Ако и само ако – Macedonisch" lang="mk" hreflang="mk" data-title="Ако и само ако" data-language-autonym="Македонски" data-language-local-name="Macedonisch" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E2%87%94" title="⇔ – Birmaans" lang="my" hreflang="my" data-title="⇔" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Birmaans" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Viss_og_berre_viss" title="Viss og berre viss – Noors - Nynorsk" lang="nn" hreflang="nn" data-title="Viss og berre viss" data-language-autonym="Norsk nynorsk" data-language-local-name="Noors - Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%9C%E0%A9%87_%E0%A8%85%E0%A8%A4%E0%A9%87_%E0%A8%B8%E0%A8%BF%E0%A8%B0%E0%A8%AB_%E0%A8%9C%E0%A9%87" title="ਜੇ ਅਤੇ ਸਿਰਫ ਜੇ – Punjabi" lang="pa" hreflang="pa" data-title="ਜੇ ਅਤੇ ਸਿਰਫ ਜੇ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/R%C3%B3wnowa%C5%BCno%C5%9B%C4%87" title="Równoważność – Pools" lang="pl" hreflang="pl" data-title="Równoważność" data-language-autonym="Polski" data-language-local-name="Pools" 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/Se_e_somente_se" title="Se e somente se – Portugees" lang="pt" hreflang="pt" data-title="Se e somente se" data-language-autonym="Português" data-language-local-name="Portugees" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Dac%C4%83_%C8%99i_numai_dac%C4%83" title="Dacă și numai dacă – Roemeens" lang="ro" hreflang="ro" data-title="Dacă și numai dacă" data-language-autonym="Română" data-language-local-name="Roemeens" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A2%D0%BE%D0%B3%D0%B4%D0%B0_%D0%B8_%D1%82%D0%BE%D0%BB%D1%8C%D0%BA%D0%BE_%D1%82%D0%BE%D0%B3%D0%B4%D0%B0" title="Тогда и только тогда – Russisch" lang="ru" hreflang="ru" data-title="Тогда и только тогда" data-language-autonym="Русский" data-language-local-name="Russisch" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Ako_i_samo_ako" title="Ako i samo ako – Servo-Kroatisch" lang="sh" hreflang="sh" data-title="Ako i samo ako" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Servo-Kroatisch" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/If_and_only_if" title="If and only if – Simple English" lang="en-simple" hreflang="en-simple" data-title="If and only if" 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-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%90%D0%BA%D0%BE_%D0%B8_%D1%81%D0%B0%D0%BC%D0%BE_%D0%B0%D0%BA%D0%BE" title="Ако и само ако – Servisch" lang="sr" hreflang="sr" data-title="Ако и само ако" data-language-autonym="Српски / srpski" data-language-local-name="Servisch" 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/Om_och_endast_om" title="Om och endast om – Zweeds" lang="sv" hreflang="sv" data-title="Om och endast om" data-language-autonym="Svenska" data-language-local-name="Zweeds" 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%B9%87%E0%B8%95%E0%B9%88%E0%B8%AD%E0%B9%80%E0%B8%A1%E0%B8%B7%E0%B9%88%E0%B8%AD" title="ก็ต่อเมื่อ – Thai" lang="th" hreflang="th" data-title="ก็ต่อเมื่อ" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Ancak_ve_ancak" title="Ancak ve ancak – Turks" lang="tr" hreflang="tr" data-title="Ancak ve ancak" data-language-autonym="Türkçe" data-language-local-name="Turks" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D0%BE%D0%B4%D1%96_%D0%B9_%D0%BB%D0%B8%D1%88%D0%B5_%D1%82%D0%BE%D0%B4%D1%96" title="Тоді й лише тоді – Oekraïens" lang="uk" hreflang="uk" data-title="Тоді й лише тоді" data-language-autonym="Українська" data-language-local-name="Oekraïens" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A7%DA%AF%D8%B1_%D8%A8%D8%B4%D8%B1%D8%B7_%D8%A7%DA%AF%D8%B1" title="اگر بشرط اگر – Urdu" lang="ur" hreflang="ur" data-title="اگر بشرط اگر" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Khi_v%C3%A0_ch%E1%BB%89_khi" title="Khi và chỉ khi – Vietnamees" lang="vi" hreflang="vi" data-title="Khi và chỉ khi" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamees" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%BD%93%E4%B8%94%E4%BB%85%E5%BD%93" title="当且仅当 – Chinees" lang="zh" hreflang="zh" data-title="当且仅当" data-language-autonym="中文" data-language-local-name="Chinees" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/N%C4%81_kiam_ta_n%C4%81" title="Nā kiam ta nā – Minnanyu" lang="nan" hreflang="nan" data-title="Nā kiam ta nā" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnanyu" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E8%8B%A5%E4%B8%94%E5%94%AF%E8%8B%A5" title="若且唯若 – Kantonees" lang="yue" hreflang="yue" data-title="若且唯若" data-language-autonym="粵語" data-language-local-name="Kantonees" class="interlanguage-link-target"><span>粵語</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/Q949972#sitelinks-wikipedia" title="Taalkoppelingen bewerken" class="wbc-editpage">Koppelingen bewerken</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Naamruimten"> <div 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class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">naar zijbalk verplaatsen</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">verbergen</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">Uit Wikipedia, de vrije encyclopedie</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="nl" dir="ltr"><p><b>Dan en slechts dan als</b> (afkorting: <b>desda</b>) is in de <a href="/wiki/Wiskunde" title="Wiskunde">wiskunde</a> en in de <a href="/wiki/Logica_(wetenschap)" class="mw-redirect" title="Logica (wetenschap)">logica</a> een algemeen gebruikte uitdrukking om <a href="/wiki/Logische_equivalentie" title="Logische equivalentie">equivalentie</a> van twee uitspraken aan te geven. Deze relatie tussen uitspraken wordt ook <b>bi-implicatie</b> of <b>wederzijdse implicatie</b> genoemd. </p><p>Gelijkwaardig zijn: </p> <ul><li>P ⇔ Q</li> <li><i>P</i> (geldt) dan en slechts dan als <i>Q</i> (geldt)</li> <li><i>P</i> (geldt) dan en alleen dan als <i>Q</i> (geldt)</li> <li><i>P</i> (geldt) als en slechts als <i>Q</i> (geldt)</li> <li><i>P</i> (geldt) als en alleen als <i>Q</i> (geldt)</li> <li><i>P</i> is een <a href="/wiki/Noodzakelijke_en_voldoende_voorwaarde" title="Noodzakelijke en voldoende voorwaarde">noodzakelijke en voldoende voorwaarde</a> voor <i>Q</i></li> <li><i>P</i> en <i>Q</i> zijn allebei waar, óf <i>P</i> en <i>Q</i> zijn allebei onwaar</li></ul> <p>Afkortingen: <b>asa</b> (het in België meer gebruikte <b>als en slechts als</b>), <b>aeaa</b> (als en alleen als). In Engelstalige literatuur gebruikt men de uitdrukking <i>iff</i> (voor <i>if and only if</i>). </p><p>Soms staat er tussen 'dan en slechts dan' en 'als' nog iets, zoals </p> <dl><dd>'een verzameling reële getallen is dan en slechts dan compact als deze gesloten en begrensd is'</dd></dl> <p>als variant op </p> <dl><dd>'een verzameling reële getallen is compact dan en slechts dan als deze gesloten en begrensd is'</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Waarheidstabel">Waarheidstabel</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dan_en_slechts_dan_als&veaction=edit&section=1" title="Bewerk dit kopje: Waarheidstabel" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dan_en_slechts_dan_als&action=edit&section=1" title="De broncode bewerken van de sectie: Waarheidstabel"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>De waarheidstabel voor de bi-implicatie is als volgt: <br /> (T = True = waar, F = False = onwaar) </p> <table class="wikitable" style="margin:1em auto; text-align:center; width:30%"> <tbody><tr> <th style="width:30%"><i>p</i> </th> <th style="width:30%"><i>q</i></th> <th style="width:1%; background:#e0e0f8"> </th> <th style="width:30%"><i>p</i> ⇔ <i>q</i> </th></tr> <tr> <td>T</td> <td>T</td> <td style="background:#e0e0f8"></td> <td>T </td></tr> <tr> <td>T</td> <td style="background:papayawhip">F</td> <td style="background:#e0e0f8"> </td> <td style="background:papayawhip">F </td></tr> <tr> <td style="background:papayawhip">F</td> <td>T</td> <td style="background:#e0e0f8"> </td> <td style="background:papayawhip">F </td></tr> <tr> <td style="background:papayawhip">F</td> <td style="background:papayawhip">F </td> <td style="background:#e0e0f8"></td> <td>T </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Voorbeeld">Voorbeeld</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dan_en_slechts_dan_als&veaction=edit&section=2" title="Bewerk dit kopje: Voorbeeld" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dan_en_slechts_dan_als&action=edit&section=2" title="De broncode bewerken van de sectie: Voorbeeld"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Een voorbeeld van het gebruik van '<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>': </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 x^{2}=9\Leftrightarrow x=3\!\,\vee x=-3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>9</mn> <mo stretchy="false">⇔</mo> <mi>x</mi> <mo>=</mo> <mn>3</mn> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>∨</mo> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}=9\Leftrightarrow x=3\!\,\vee x=-3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/848cf135fc6f8fe02c150bfdf35613da37ec644e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:25.831ex; height:2.843ex;" alt="{\displaystyle x^{2}=9\Leftrightarrow x=3\!\,\vee x=-3}"></span>.</dd></dl> <p>Dit betekent twee dingen, namelijk enerzijds: </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 x^{2}=9\Rightarrow x=3\!\,\vee x=-3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>9</mn> <mo stretchy="false">⇒</mo> <mi>x</mi> <mo>=</mo> <mn>3</mn> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>∨</mo> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}=9\Rightarrow x=3\!\,\vee x=-3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96ddb965ed5c80d7b7af973cfccc3dba9ab9afc4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:25.831ex; height:2.843ex;" alt="{\displaystyle x^{2}=9\Rightarrow x=3\!\,\vee x=-3}"></span>.</dd> <dd>dat wil zeggen: Uit het feit dat x in het <a href="/wiki/Kwadraat" title="Kwadraat">kwadraat</a> 9 oplevert, volgt dat x gelijk is aan 3 of aan −3. Immers, er zijn geen andere <a href="/wiki/Getal_(wiskunde)" title="Getal (wiskunde)">getallen</a> die gekwadrateerd 9 opleveren.</dd></dl> <p>en anderzijds </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 x=3\!\,\vee x=-3\Rightarrow x^{2}=9}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mn>3</mn> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> <mo>∨</mo> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mn>3</mn> <mo stretchy="false">⇒</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>9</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x=3\!\,\vee x=-3\Rightarrow x^{2}=9}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8508b78708826266acdfd6a66d635b00adc3c075" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:25.831ex; height:2.843ex;" alt="{\displaystyle x=3\!\,\vee x=-3\Rightarrow x^{2}=9}"></span>.</dd> <dd>dat wil zeggen: Uit het feit dat x gelijk is aan 3 of aan −3, volgt dat x in het <a href="/wiki/Kwadraat" title="Kwadraat">kwadraat</a> 9 is. Immers, het kwadraat van 3 zowel als van −3 is 9.</dd></dl> <p>Overigens geldt ook: </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 x=3\Rightarrow x^{2}=9}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mn>3</mn> <mo stretchy="false">⇒</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>9</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x=3\Rightarrow x^{2}=9}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c64d638cb205665db9804fc18b590b02209d3157" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:15.85ex; height:2.676ex;" alt="{\displaystyle x=3\Rightarrow x^{2}=9}"></span>.</dd></dl> <p>Dit betekent: uit het feit dat x gelijk is aan 3, volgt dat x in het kwadraat 9 is. Hier mag <i>niet</i> het symbool '<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>' gebruikt worden, want uit x<sup>2</sup> = 9 hoeft niet te volgen dat x = 3. Immers ook x = −3 is mogelijk. </p> <div class="mw-heading mw-heading2"><h2 id="Zie_ook">Zie ook</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dan_en_slechts_dan_als&veaction=edit&section=3" title="Bewerk dit kopje: Zie ook" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dan_en_slechts_dan_als&action=edit&section=3" title="De broncode bewerken van de sectie: Zie ook"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Noodzakelijke_en_voldoende_voorwaarde" title="Noodzakelijke en voldoende voorwaarde">noodzakelijke en voldoende voorwaarde</a></li></ul>    </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="">Overgenomen van "<a dir="ltr" href="https://nl.wikipedia.org/w/index.php?title=Dan_en_slechts_dan_als&oldid=68360417">https://nl.wikipedia.org/w/index.php?title=Dan_en_slechts_dan_als&oldid=68360417</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Categorie:Alles" title="Categorie:Alles">Categorieën</a>: <ul><li><a href="/wiki/Categorie:Logica" title="Categorie:Logica">Logica</a></li><li><a href="/wiki/Categorie:Wiskundige_terminologie" title="Categorie:Wiskundige terminologie">Wiskundige terminologie</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"> Deze pagina is voor het laatst bewerkt op 10 nov 2024 om 09:39.</li> <li id="footer-info-copyright">De tekst is beschikbaar onder de licentie <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/deed.nl">Creative Commons Naamsvermelding/Gelijk delen</a>, er kunnen aanvullende voorwaarden van toepassing zijn. 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