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title="Viquipèdia (ca)"> <link rel="EditURI" type="application/rsd+xml" href="//ca.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://ca.wikipedia.org/wiki/Complementari"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.ca"> <link rel="alternate" type="application/atom+xml" title="Canal de sindicació Atom Viquipèdia" href="/w/index.php?title=Especial:Canvis_recents&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Complementari rootpage-Complementari skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Vés al contingut</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Lloc"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Menú principal" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Menú principal</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Menú principal</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">mou a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">amaga</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navegació </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Portada" title="Visiteu la pàgina principal [z]" accesskey="z"><span>Portada</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Especial:Article_aleatori" title="Carrega una pàgina a l’atzar [x]" accesskey="x"><span>Article a l'atzar</span></a></li><li id="n-Articles-de-qualitat" class="mw-list-item"><a href="/wiki/Viquip%C3%A8dia:Articles_de_qualitat"><span>Articles de qualitat</span></a></li> </ul> </div> </div> <div id="p-Comunitat" class="vector-menu mw-portlet mw-portlet-Comunitat" > <div class="vector-menu-heading"> Comunitat </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-portal" class="mw-list-item"><a href="/wiki/Viquip%C3%A8dia:Portal" title="Sobre el projecte, què podeu fer, on trobareu les coses"><span>Portal viquipedista</span></a></li><li id="n-Agenda-d'actes" class="mw-list-item"><a href="/wiki/Viquip%C3%A8dia:Trobades"><span>Agenda d'actes</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Especial:Canvis_recents" title="Una llista dels canvis recents al wiki [r]" accesskey="r"><span>Canvis recents</span></a></li><li id="n-La-taverna" class="mw-list-item"><a href="/wiki/Viquip%C3%A8dia:La_taverna"><span>La taverna</span></a></li><li id="n-contactpage" class="mw-list-item"><a href="/wiki/Viquip%C3%A8dia:Contacte"><span>Contacte</span></a></li><li id="n-Xat" class="mw-list-item"><a href="/wiki/Viquip%C3%A8dia:Canals_IRC"><span>Xat</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Viquip%C3%A8dia:Ajuda" title="El lloc per a saber més coses"><span>Ajuda</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Portada" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Viquipèdia" src="/static/images/mobile/copyright/wikipedia-wordmark-ca.svg" style="width: 7.5em; height: 1.4375em;"> <img class="mw-logo-tagline" alt="l'Enciclopèdia Lliure" src="/static/images/mobile/copyright/wikipedia-tagline-ca.svg" width="120" height="14" style="width: 7.5em; height: 0.875em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Especial:Cerca" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Cerca a la Viquipèdia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Cerca</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Cerca a Viquipèdia" aria-label="Cerca a Viquipèdia" autocapitalize="sentences" title="Cerca a la Viquipèdia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Especial:Cerca"> </div> <button class="cdx-button cdx-search-input__end-button">Cerca</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Eines personals"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Aparença"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Aparença" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Aparença</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_ca.wikipedia.org&uselang=ca" class=""><span>Donatius</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Especial:Crea_compte&returnto=Complementari" title="Us animem a crear un compte i iniciar una sessió, encara que no és obligatori" class=""><span>Crea un compte</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Especial:Registre_i_entrada&returnto=Complementari" title="Us animem a registrar-vos, però no és obligatori [o]" accesskey="o" class=""><span>Inicia la sessió</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Més opcions" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Eines personals" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Eines personals</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Menú d'usuari" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_ca.wikipedia.org&uselang=ca"><span>Donatius</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Especial:Crea_compte&returnto=Complementari" title="Us animem a crear un compte i iniciar una sessió, encara que no és obligatori"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Crea un compte</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Especial:Registre_i_entrada&returnto=Complementari" title="Us animem a registrar-vos, però no és obligatori [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Inicia la sessió</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pàgines per a editors no registrats <a href="/wiki/Ajuda:Introducci%C3%B3" aria-label="Vegeu més informació sobre l'edició"><span>més informació</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Especial:Contribucions_pr%C3%B2pies" title="Una llista de les modificacions fetes des d'aquesta adreça IP [y]" accesskey="y"><span>Contribucions</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Especial:Discussi%C3%B3_personal" title="Discussió sobre les edicions per aquesta adreça ip. [n]" accesskey="n"><span>Discussió per aquest IP</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Lloc"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Contingut" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Contingut</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mou a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">amaga</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Inici</div> </a> </li> <li id="toc-Propietats" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Propietats"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Propietats</span> </div> </a> <button aria-controls="toc-Propietats-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Commuta la subsecció Propietats</span> </button> <ul id="toc-Propietats-sublist" class="vector-toc-list"> <li id="toc-Complementari_d'un_conjunt_respecte_a_si_mateix" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Complementari_d'un_conjunt_respecte_a_si_mateix"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Complementari d'un conjunt respecte a si mateix</span> </div> </a> <ul id="toc-Complementari_d'un_conjunt_respecte_a_si_mateix-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Relació_amb_la_intersecció" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Relació_amb_la_intersecció"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Relació amb la intersecció</span> </div> </a> <ul id="toc-Relació_amb_la_intersecció-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Propietat_involutiva" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Propietat_involutiva"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Propietat involutiva</span> </div> </a> <ul id="toc-Propietat_involutiva-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Propietats_de_complementarietat" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Propietats_de_complementarietat"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Propietats de complementarietat</span> </div> </a> <ul id="toc-Propietats_de_complementarietat-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lleis_de_De_Morgan" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lleis_de_De_Morgan"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.5</span> <span>Lleis de De Morgan</span> </div> </a> <ul id="toc-Lleis_de_De_Morgan-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contingut" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Commuta la taula de continguts." > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Commuta la taula de continguts.</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Complementari</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="Vés a un article en una altra llengua. Disponible en 48 llengües" > <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-48" 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">48 llengües</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%A8%E1%8B%8D%E1%8C%AD_%E1%88%B5%E1%89%A5%E1%88%B5%E1%89%A5" title="የውጭ ስብስብ - amhàric" lang="am" hreflang="am" data-title="የውጭ ስብስብ" data-language-autonym="አማርኛ" data-language-local-name="amhàric" 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/%D9%85%D8%AC%D9%85%D9%88%D8%B9%D8%A9_%D9%85%D9%83%D9%85%D9%84%D8%A9_(%D9%86%D8%B8%D8%B1%D9%8A%D8%A9_%D8%A7%D9%84%D9%85%D8%AC%D9%85%D9%88%D8%B9%D8%A7%D8%AA)" title="مجموعة مكملة (نظرية المجموعات) - àrab" lang="ar" hreflang="ar" data-title="مجموعة مكملة (نظرية المجموعات)" data-language-autonym="العربية" data-language-local-name="àrab" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%94%D0%B0%D0%BF%D0%B0%D1%9E%D0%BD%D0%B5%D0%BD%D0%BD%D0%B5_%D0%BC%D0%BD%D0%BE%D1%81%D1%82%D0%B2%D0%B0%D1%9E" title="Дапаўненне мностваў - belarús" lang="be" hreflang="be" data-title="Дапаўненне мностваў" data-language-autonym="Беларуская" data-language-local-name="belarús" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B7%D0%BB%D0%B8%D0%BA%D0%B0_(%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D0%BD%D0%B0_%D0%BC%D0%BD%D0%BE%D0%B6%D0%B5%D1%81%D1%82%D0%B2%D0%B0%D1%82%D0%B0)" title="Разлика (теория на множествата) - búlgar" lang="bg" hreflang="bg" data-title="Разлика (теория на множествата)" data-language-autonym="Български" data-language-local-name="búlgar" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Dopln%C4%9Bk_mno%C5%BEiny" title="Doplněk množiny - txec" lang="cs" hreflang="cs" data-title="Doplněk množiny" data-language-autonym="Čeština" data-language-local-name="txec" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%99%D1%8B%D1%88%D1%81%D0%B5%D0%BD_%D0%BA%C4%83%D0%BB%D0%B0%D1%80%D0%BD%C4%83%D0%BB%C4%83%D1%85%C4%95" title="Йышсен кăларнăлăхĕ - txuvaix" lang="cv" hreflang="cv" data-title="Йышсен кăларнăлăхĕ" data-language-autonym="Чӑвашла" data-language-local-name="txuvaix" 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/Cyflenwad_(setiau)" title="Cyflenwad (setiau) - gal·lès" lang="cy" hreflang="cy" data-title="Cyflenwad (setiau)" data-language-autonym="Cymraeg" data-language-local-name="gal·lès" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Komplement_(Mengenlehre)" title="Komplement (Mengenlehre) - alemany" lang="de" hreflang="de" data-title="Komplement (Mengenlehre)" data-language-autonym="Deutsch" data-language-local-name="alemany" 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%A3%CF%85%CE%BC%CF%80%CE%BB%CE%AE%CF%81%CF%89%CE%BC%CE%B1_(%CE%B8%CE%B5%CF%89%CF%81%CE%AF%CE%B1_%CF%83%CF%85%CE%BD%CF%8C%CE%BB%CF%89%CE%BD)" title="Συμπλήρωμα (θεωρία συνόλων) - grec" lang="el" hreflang="el" data-title="Συμπλήρωμα (θεωρία συνόλων)" data-language-autonym="Ελληνικά" data-language-local-name="grec" 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/Complement_(set_theory)" title="Complement (set theory) - anglès" lang="en" hreflang="en" data-title="Complement (set theory)" data-language-autonym="English" data-language-local-name="anglès" 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/Komplemento_(aroteorio)" title="Komplemento (aroteorio) - esperanto" lang="eo" hreflang="eo" data-title="Komplemento (aroteorio)" 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/Complemento_de_un_conjunto" title="Complemento de un conjunto - espanyol" lang="es" hreflang="es" data-title="Complemento de un conjunto" data-language-autonym="Español" data-language-local-name="espanyol" 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/T%C3%A4iend_(hulgateooria)" title="Täiend (hulgateooria) - estonià" lang="et" hreflang="et" data-title="Täiend (hulgateooria)" data-language-autonym="Eesti" data-language-local-name="estonià" 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/Osagarri_(multzo-teoria)" title="Osagarri (multzo-teoria) - basc" lang="eu" hreflang="eu" data-title="Osagarri (multzo-teoria)" data-language-autonym="Euskara" data-language-local-name="basc" 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/%D9%85%D8%AA%D9%85%D9%85_(%D9%86%D8%B8%D8%B1%DB%8C%D9%87_%D9%85%D8%AC%D9%85%D9%88%D8%B9%D9%87%E2%80%8C%D9%87%D8%A7)" title="متمم (نظریه مجموعه‌ها) - persa" lang="fa" hreflang="fa" data-title="متمم (نظریه مجموعه‌ها)" data-language-autonym="فارسی" data-language-local-name="persa" 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/Komplementti_(joukko-oppi)" title="Komplementti (joukko-oppi) - finès" lang="fi" hreflang="fi" data-title="Komplementti (joukko-oppi)" data-language-autonym="Suomi" data-language-local-name="finès" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Compl%C3%A9mentaire_(th%C3%A9orie_des_ensembles)" title="Complémentaire (théorie des ensembles) - francès" lang="fr" hreflang="fr" data-title="Complémentaire (théorie des ensembles)" data-language-autonym="Français" data-language-local-name="francès" 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/Complementario_(conxuntos)" title="Complementario (conxuntos) - gallec" lang="gl" hreflang="gl" data-title="Complementario (conxuntos)" data-language-autonym="Galego" data-language-local-name="gallec" 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%9E%D7%A9%D7%9C%D7%99%D7%9D_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="משלים (מתמטיקה) - hebreu" lang="he" hreflang="he" data-title="משלים (מתמטיקה)" data-language-autonym="עברית" data-language-local-name="hebreu" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Komplement_skupa" title="Komplement skupa - croat" lang="hr" hreflang="hr" data-title="Komplement skupa" data-language-autonym="Hrvatski" data-language-local-name="croat" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Komplemen_(teori_himpunan)" title="Komplemen (teori himpunan) - indonesi" lang="id" hreflang="id" data-title="Komplemen (teori himpunan)" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesi" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Fyllimengi" title="Fyllimengi - islandès" lang="is" hreflang="is" data-title="Fyllimengi" data-language-autonym="Íslenska" data-language-local-name="islandès" 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/Insieme_complemento" title="Insieme complemento - italià" lang="it" hreflang="it" data-title="Insieme complemento" data-language-autonym="Italiano" data-language-local-name="italià" 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%B7%AE%E9%9B%86%E5%90%88" title="差集合 - japonès" lang="ja" hreflang="ja" data-title="差集合" data-language-autonym="日本語" data-language-local-name="japonès" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%97%AC%EC%A7%91%ED%95%A9" title="여집합 - coreà" lang="ko" hreflang="ko" data-title="여집합" data-language-autonym="한국어" data-language-local-name="coreà" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BC%D0%BF%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82" title="Комплемент - macedoni" lang="mk" hreflang="mk" data-title="Комплемент" data-language-autonym="Македонски" data-language-local-name="macedoni" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Pelengkap_(teori_set)" title="Pelengkap (teori set) - malai" lang="ms" hreflang="ms" data-title="Pelengkap (teori set)" data-language-autonym="Bahasa Melayu" data-language-local-name="malai" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Complement_(verzamelingenleer)" title="Complement (verzamelingenleer) - neerlandès" lang="nl" hreflang="nl" data-title="Complement (verzamelingenleer)" data-language-autonym="Nederlands" data-language-local-name="neerlandès" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Komplement_i_mengdel%C3%A6re" title="Komplement i mengdelære - noruec nynorsk" lang="nn" hreflang="nn" data-title="Komplement i mengdelære" data-language-autonym="Norsk nynorsk" data-language-local-name="noruec nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Komplement_(mengdel%C3%A6re)" title="Komplement (mengdelære) - noruec bokmål" lang="nb" hreflang="nb" data-title="Komplement (mengdelære)" data-language-autonym="Norsk bokmål" data-language-local-name="noruec bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Ensemble_complementari" title="Ensemble complementari - occità" lang="oc" hreflang="oc" data-title="Ensemble complementari" data-language-autonym="Occitan" data-language-local-name="occità" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Dope%C5%82nienie_zbioru" title="Dopełnienie zbioru - polonès" lang="pl" hreflang="pl" data-title="Dopełnienie zbioru" data-language-autonym="Polski" data-language-local-name="polonès" 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/Complementar" title="Complementar - portuguès" lang="pt" hreflang="pt" data-title="Complementar" data-language-autonym="Português" data-language-local-name="portuguès" 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/Complementar%C4%83" title="Complementară - romanès" lang="ro" hreflang="ro" data-title="Complementară" data-language-autonym="Română" data-language-local-name="romanès" 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%A0%D0%B0%D0%B7%D0%BD%D0%BE%D1%81%D1%82%D1%8C_%D0%BC%D0%BD%D0%BE%D0%B6%D0%B5%D1%81%D1%82%D0%B2" title="Разность множеств - rus" lang="ru" hreflang="ru" data-title="Разность множеств" data-language-autonym="Русский" data-language-local-name="rus" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Doplnok_(mno%C5%BEiny)" title="Doplnok (množiny) - eslovac" lang="sk" hreflang="sk" data-title="Doplnok (množiny)" data-language-autonym="Slovenčina" data-language-local-name="eslovac" 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/Komplement_mno%C5%BEice" title="Komplement množice - eslovè" lang="sl" hreflang="sl" data-title="Komplement množice" data-language-autonym="Slovenščina" data-language-local-name="eslovè" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Komplement" title="Komplement - suec" lang="sv" hreflang="sv" data-title="Komplement" data-language-autonym="Svenska" data-language-local-name="suec" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A8%E0%AE%BF%E0%AE%B0%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AF%81_%E0%AE%95%E0%AE%A3%E0%AE%AE%E0%AF%8D" title="நிரப்பு கணம் - tàmil" lang="ta" hreflang="ta" data-title="நிரப்பு கணம்" data-language-autonym="தமிழ்" data-language-local-name="tàmil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%AA%E0%B9%88%E0%B8%A7%E0%B8%99%E0%B9%80%E0%B8%95%E0%B8%B4%E0%B8%A1%E0%B9%80%E0%B8%95%E0%B9%87%E0%B8%A1" title="ส่วนเติมเต็ม - tai" lang="th" hreflang="th" data-title="ส่วนเติมเต็ม" data-language-autonym="ไทย" data-language-local-name="tai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Komplemento_(teorya_ng_pangkat)" title="Komplemento (teorya ng pangkat) - tagal" lang="tl" hreflang="tl" data-title="Komplemento (teorya ng pangkat)" data-language-autonym="Tagalog" data-language-local-name="tagal" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%94%D0%BE%D0%BF%D0%BE%D0%B2%D0%BD%D0%B5%D0%BD%D0%BD%D1%8F_%D0%BC%D0%BD%D0%BE%D0%B6%D0%B8%D0%BD" title="Доповнення множин - ucraïnès" lang="uk" hreflang="uk" data-title="Доповнення множин" data-language-autonym="Українська" data-language-local-name="ucraïnès" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Ph%E1%BA%A7n_b%C3%B9_(l%C3%BD_thuy%E1%BA%BFt_t%E1%BA%ADp_h%E1%BB%A3p)" title="Phần bù (lý thuyết tập hợp) - vietnamita" lang="vi" hreflang="vi" data-title="Phần bù (lý thuyết tập hợp)" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamita" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E8%A1%A5%E9%9B%86" title="补集 - xinès wu" lang="wuu" hreflang="wuu" data-title="补集" data-language-autonym="吴语" data-language-local-name="xinès wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xal mw-list-item"><a href="https://xal.wikipedia.org/wiki/%D0%9D%D0%B5%D0%BC%D0%B3%D0%B8%D0%BD" title="Немгин - calmuc" lang="xal" hreflang="xal" data-title="Немгин" data-language-autonym="Хальмг" data-language-local-name="calmuc" class="interlanguage-link-target"><span>Хальмг</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%A1%A5%E9%9B%86" title="补集 - xinès" lang="zh" hreflang="zh" data-title="补集" data-language-autonym="中文" data-language-local-name="xinès" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E8%A3%9C%E9%9B%86" title="補集 - xinès clàssic" lang="lzh" hreflang="lzh" data-title="補集" data-language-autonym="文言" data-language-local-name="xinès clàssic" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%B7%AE%E9%9B%86" title="差集 - cantonès" lang="yue" hreflang="yue" data-title="差集" data-language-autonym="粵語" data-language-local-name="cantonès" 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/Q242767#sitelinks-wikipedia" title="Modifica enllaços interlingües" class="wbc-editpage">Modifica els enllaços</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="Espais de noms"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Complementari" title="Vegeu el contingut de la pàgina [c]" accesskey="c"><span>Pàgina</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Discussi%C3%B3:Complementari&action=edit&redlink=1" rel="discussion" class="new" title="Discussió sobre el contingut d'aquesta pàgina (encara no existeix) [t]" accesskey="t"><span>Discussió</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" 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class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Complementari"><span>Mostra</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Complementari&action=edit" title="Modifica el codi font d'aquesta pàgina [e]" accesskey="e"><span>Modifica</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Complementari&action=history" title="Versions antigues d'aquesta pàgina [h]" accesskey="h"><span>Mostra l'historial</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Eines de la pàgina"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Eines" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Eines</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Eines</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">mou a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">amaga</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Més opcions" > <div class="vector-menu-heading"> Accions </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Complementari"><span>Mostra</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Complementari&action=edit" title="Modifica el codi font d'aquesta pàgina [e]" accesskey="e"><span>Modifica</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Complementari&action=history"><span>Mostra l'historial</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Especial:Enlla%C3%A7os/Complementari" title="Una llista de totes les pàgines wiki que enllacen amb aquesta [j]" accesskey="j"><span>Què hi enllaça</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Especial:Seguiment/Complementari" rel="nofollow" title="Canvis recents a pàgines enllaçades des d'aquesta pàgina [k]" accesskey="k"><span>Canvis relacionats</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Especial:P%C3%A0gines_especials" title="Llista totes les pàgines especials [q]" accesskey="q"><span>Pàgines especials</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Complementari&oldid=33726346" title="Enllaç permanent a aquesta revisió de la pàgina"><span>Enllaç permanent</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Complementari&action=info" title="Més informació sobre aquesta pàgina"><span>Informació de la pàgina</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Especial:Citau&page=Complementari&id=33726346&wpFormIdentifier=titleform" title="Informació sobre com citar aquesta pàgina"><span>Citau aquest article</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Especial:UrlShortener&url=https%3A%2F%2Fca.wikipedia.org%2Fwiki%2FComplementari"><span>Obtén una URL abreujada</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Especial:QrCode&url=https%3A%2F%2Fca.wikipedia.org%2Fwiki%2FComplementari"><span>Descarrega el codi QR</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Imprimeix/exporta </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Especial:Llibre&bookcmd=book_creator&referer=Complementari"><span>Crea un llibre</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Especial:DownloadAsPdf&page=Complementari&action=show-download-screen"><span>Baixa com a PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Complementari&printable=yes" title="Versió per a impressió d'aquesta pàgina [p]" accesskey="p"><span>Versió per a impressora</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> En altres projectes </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q242767" title="Enllaç a l'element del repositori de dades connectat [g]" accesskey="g"><span>Element a Wikidata</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Eines de la pàgina"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Aparença"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Aparença</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">mou a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">amaga</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">De la Viquipèdia, l'enciclopèdia lliure</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="ca" dir="ltr"><p>S'anomena <b>conjunt complementari</b> d'un <a href="/wiki/Conjunt" title="Conjunt">conjunt</a> <i>A</i> respecte d'un conjunt <i>C</i> el conjunt <a href="/wiki/Difer%C3%A8ncia" title="Diferència">diferència</a> <i>C</i>∖<i>A</i> (també escrit <i>C</i>−<i>A</i>). De vegades es representa com Ā. </p><p>Per exemple, si C = {1, 2, 3, ..., 9, 10} i A = {3, 4, 5, 6}, llavors Ā = {1, 2, 7, 8, 9, 10}. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Propietats">Propietats</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complementari&action=edit&section=1" title="Modifica la secció: Propietats"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Complementari_d'un_conjunt_respecte_a_si_mateix"><span id="Complementari_d.27un_conjunt_respecte_a_si_mateix"></span>Complementari d'un conjunt respecte a si mateix</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complementari&action=edit&section=2" title="Modifica la secció: Complementari d'un conjunt respecte a si mateix"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>El complementari d'un conjunt C respecte a si mateix és el conjunt buit. </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 {\overline {C}}=C\setminus C=\emptyset }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo>=</mo> <mi>C</mi> <mo class="MJX-variant">∖</mo> <mi>C</mi> <mo>=</mo> <mi mathvariant="normal">∅</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {C}}=C\setminus C=\emptyset }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86f0179574e19672e7fa8f524d09423f1d583b80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.036ex; height:3.509ex;" alt="{\displaystyle {\overline {C}}=C\setminus C=\emptyset }"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Relació_amb_la_intersecció"><span id="Relaci.C3.B3_amb_la_intersecci.C3.B3"></span>Relació amb la <a href="/wiki/Intersecci%C3%B3" title="Intersecció">intersecció</a></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complementari&action=edit&section=3" title="Modifica la secció: Relació amb la intersecció"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <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\setminus B=A\cap {\overline {B}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo class="MJX-variant">∖</mo> <mi>B</mi> <mo>=</mo> <mi>A</mi> <mo>∩</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo accent="false">¯</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\setminus B=A\cap {\overline {B}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23ba53af4070956a331b57f89f86180a91f700d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.005ex; height:3.509ex;" alt="{\displaystyle A\setminus B=A\cap {\overline {B}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Propietat_involutiva">Propietat involutiva</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complementari&action=edit&section=4" title="Modifica la secció: Propietat involutiva"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>El complementari del complementari d'un conjunt és el mateix conjunt. </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 {\overline {\overline {A}}}=A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mover> <mi>A</mi> <mo accent="false">¯</mo> </mover> <mo accent="false">¯</mo> </mover> </mrow> <mo>=</mo> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {\overline {A}}}=A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0820a1e2978140433ac7033854eae4d2d859b027" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.815ex; height:3.843ex;" alt="{\displaystyle {\overline {\overline {A}}}=A}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Propietats_de_complementarietat">Propietats de complementarietat</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complementari&action=edit&section=5" title="Modifica la secció: Propietats de complementarietat"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Per tal que dos conjunts siguin complementaris s'han de complir les propietats següents: </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 {\overline {A}}\cup A=C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo>∪</mo> <mi>A</mi> <mo>=</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {A}}\cup A=C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9a76f437e90d9bb56d3755e5c7fc1750e8c702e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.049ex; height:3.009ex;" alt="{\displaystyle {\overline {A}}\cup A=C}"></span></dd></dl> <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 {\overline {A}}\cap A=\emptyset }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo>∩</mo> <mi>A</mi> <mo>=</mo> <mi mathvariant="normal">∅</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {A}}\cap A=\emptyset }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cef7a43bb5ab38eac101ee8056545b34c1b12a24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:10.445ex; height:3.176ex;" alt="{\displaystyle {\overline {A}}\cap A=\emptyset }"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Lleis_de_De_Morgan">Lleis de De Morgan</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Complementari&action=edit&section=6" title="Modifica la secció: Lleis de De Morgan"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <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 {\overline {(A\cup B)}}={\overline {A}}\cap {\overline {B}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo>∪</mo> <mi>B</mi> <mo stretchy="false">)</mo> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo>∩</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo accent="false">¯</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {(A\cup B)}}={\overline {A}}\cap {\overline {B}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f09f507298d4c4c98fe293b39a4792f18458293" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.432ex; height:3.676ex;" alt="{\displaystyle {\overline {(A\cup B)}}={\overline {A}}\cap {\overline {B}}}"></span></dd></dl> <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 {\overline {(A\cap B)}}={\overline {A}}\cup {\overline {B}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo>∩</mo> <mi>B</mi> <mo stretchy="false">)</mo> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>A</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo>∪</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>B</mi> <mo accent="false">¯</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {(A\cap B)}}={\overline {A}}\cup {\overline {B}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f88fa55216b54b6a93edad78a9402b78cb2bd6b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; 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