title: "Mengdeliar"
text: "At mengdeliar as en gr\u00fcnjleien f\u00e4\u00e4k faan't matematiik. Hat befaadet ham diarm\u00e4, h\u00fc mengden m\u00e4en\u00f6\u00f6der tuuphinge an faanen\u00f6\u00f6der ufhinge. Det spriak faan't mengdeliar woort br\u00fckt uun a algebra, analysis, geometrii, topologii an \u00f6\u00f6der matemaatisk feeg.\n\nBetiaknangen \nDet eegenskap  (as element faan) as det wichtagst ferbinjang tesken mengden. Ales, wat diar\u00fctj fulagt, san loogisk sl\u00fctjer.\n\n Apt\u00e4\u00e4lang\n At mengde m\u00e4 a elementen  bit  h\u00e4\u00e4lt det element  genau do, wan  m\u00e4 ian element  auerianstemet:\n \nDet \u00fctjsaag\n \nas likw\u00e4\u00e4rdag (ekwiwalent) m\u00e4:\n \n\n Beskriiwang\n At mengde faan , huarf\u00f6r det eegenskap  tudraapt, h\u00e4\u00e4lt en element  genau do, wan det eegenskap \u00fc\u00fcb  tudraapt:\n \n Uun a \u00fctjsaagenloogik het det:\n \n\n Dialmengde\n En mengde  as en dialmengde faan , wan arke element faan  uk element faan  as:\n\n Leesag mengde\n En mengde saner elementen as det leesag mengde. Hat woort m\u00e4  of uk  betiakent.\n\n F\u00f6r det jindial  t\u00e4\u00e4lt uk: .\n\n Gemiansoom mengde\n Diar san  mengden. Det gemiansoom mengde faan  as det mengde faan objekten, diar uun arke elementmengde faan  banen san:\n \n\n Ferianagt mengde\n Det ferianagt mengde faan  mengden as det mengde faan objekten, diar uun tumanst ian elemntmengde faan  banen san:\n \n\n Likedenang mengden\n Tau mengden san likdenang, wan diar josalew elementen banen san:\n\n Diferens an komplement \n At diferens of uk restmengde faan   an  (\"A saner B\") as det mengde faan elementen, diar uun , oober ei uun  banen san:\n \n Det diferens as uk det komplement faan B uun A:\n \n\n S\u00fcmeetrisk diferens\n Det as det jindial faan't 'gemiansoom mengde':\n \n\n Potensmengde\n At potensmengde  faan en mengde  as det mengde faan aal a 'dialmengden' faan .\n\n Karteesisk produkt\n At produktmengde faan  an  as det mengde faan aal a paaren m\u00e4 det iarst element \u00fctj  an det \u00f6\u00f6der \u00fctj :.\n\nReegeln \n(1) F\u00f6r dialmengden  t\u00e4\u00e4lt: Jo san \n refleksiif: \n antis\u00fcmeetrisk: \u00dctj  an  fulegt \n transitiif: \u00dctj  an  fulegt \n\n(2) A mengdenoperatjuunen  an  san komutatiif, asotsiatiif an distributiif:\n\n Asotsiatiifgesets:\n  an\n \n Komutatiifgesets:\n  an\n \n Distributiifgesets:\n  an\n \n De Morgan sin gesetsen:\n  an\n \n Absorptionsgesets:\n  an\n \n\n(3) Gesetsen f\u00f6r diferensmengden:\n\n Asotsiatiifgesetsen:\n  an\n \n Distributiifgesetsen:\n  an\n  an \n  an \n \n\n(4) Gesetsen f\u00f6r s\u00fcmeetrisk diferensen:\n\n Asotsiatiifgesets: \n Komutatiifgesets: \n Distributiifgesets: \n an\n\nLuke uk diar \n\n \u00dctjsaagenloogik\n\nMatematiik"