{"id":558,"date":"2017-05-29T23:11:39","date_gmt":"2017-05-29T21:11:39","guid":{"rendered":"http:\/\/theory-of-science.com\/de\/?page_id=558"},"modified":"2021-02-04T16:24:12","modified_gmt":"2021-02-04T15:24:12","slug":"uebung-12-06","status":"publish","type":"page","link":"https:\/\/theory-of-science.com\/de\/uebungen\/abschnitt-12\/uebung-12-06\/","title":{"rendered":"\u00dc12-6: Bijektion von Potenzmengen"},"content":{"rendered":"\n<p>Seien <em>X<\/em> und <em>Y<\/em> zwei Mengen und \u2118 ( <em>X<\/em> ) und&nbsp;\u2118 ( <em>Y<\/em> ) die Potenzmengen von <em>X<\/em> und <em>Y<\/em> und <em>f<\/em> : <em>X<\/em>&nbsp;\u2192 <em>Y<\/em> sei eine bijektive Funktion.<\/p>\n\n\n\n<p><strong>a)<\/strong> Seien <em>X<\/em> die Menge { 1, 2 } und <em>Y<\/em> die Menge { <em>Peter<\/em>, <em>Uta<\/em> }. Bilden sie die beiden Potenzmengen von <em>X<\/em> und <em>Y<\/em>. Definieren Sie eine Funktion <em>g<\/em> :&nbsp;\u2118 ( <em>X<\/em> )&nbsp;\u2192 \u2118 ( <em>Y<\/em> ). (Hinweis: <em>U<\/em>&nbsp;\u2286 <em>X<\/em>, <em>g<\/em> ( <em>U<\/em> ) = { <em>f<\/em> ( <em>x<\/em> ) \/ <em>x<\/em>&nbsp;\u2208 <em>U <\/em>} ).<\/p>\n\n\n\n<p><strong>b)<\/strong> Ist Ihre Funktion bijektiv? Wenn ja, warum?<br><\/p>\n\n\n<ul class=\"nav nav-pills nav-justified\">\n<li><a href=\"https:\/\/theory-of-science.com\/de\/uebungen\/abschnitt-12\/uebung-12-05\/\">&lt;&lt;&lt;<\/a><\/li>\n<li><a href=\"https:\/\/theory-of-science.com\/de\/uebungen\/abschnitt-12\/uebung-12-07\/\">&gt;&gt;&gt;<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Seien X und Y zwei Mengen und \u2118 ( X ) und&nbsp;\u2118 ( Y ) die Potenzmengen von X und Y und f : X&nbsp;\u2192 Y sei eine bijektive Funktion. a) Seien X die Menge { 1, 2 } und Y die Menge { Peter, Uta }. Bilden sie die beiden Potenzmengen von X und [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":67,"menu_order":6,"comment_status":"closed","ping_status":"closed","template":"page-fullwidth.php","meta":{"footnotes":""},"class_list":["post-558","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/pages\/558","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/comments?post=558"}],"version-history":[{"count":7,"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/pages\/558\/revisions"}],"predecessor-version":[{"id":4462,"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/pages\/558\/revisions\/4462"}],"up":[{"embeddable":true,"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/pages\/67"}],"wp:attachment":[{"href":"https:\/\/theory-of-science.com\/de\/wp-json\/wp\/v2\/media?parent=558"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}