Beweisen oder widerlegen Sie die folgenden Identitäten für Mengen:
![{\displaystyle (A\times B)\cap (A\times C)=A\times (B\cap C)}](/index.php?title=Spezial:MathShowImage&hash=a74f9f1f645cf5166792b4e74a330bb0&mode=mathml)
Dieses Beispiel hat einen unbekannten Lösungsstatus. Bitte editiere diese Seite und schreibe den dir bekannten Status ins Beispiel. Die möglichen Werte sind hier:
Vorlage:Beispiel dokumentiert. Führe folgende Änderung durch:
{{Beispiel|1=
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oder
{{Beispiel|
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zu (im Falle einer korrekten, unverifizierten Lösung "solved". Auch möglich "unsolved", "wrong", "verified_by_tutor". Alle möglichen Werte sind hier: Vorlage:Beispiel dokumentiert.)
{{Beispiel|status=solved|1=
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Dieser Lösungs Ansatzt ist falsch, es kann keine Elemententafeln für kartesische Produkte verwendet werden!
Was eine Elementtablle ist, könnt ihr im "orangen Buch", Seite 36, nachlesen.
Die Elementtabelle sieht folgendermaßen aus:
![{\displaystyle a\in A}](/index.php?title=Spezial:MathShowImage&hash=026638d7828e8287894f1cccedfaee9c&mode=mathml) |
![{\displaystyle b\in B}](/index.php?title=Spezial:MathShowImage&hash=2e21d7a762860f92a0775ddc31e8203b&mode=mathml) |
![{\displaystyle c\in C}](/index.php?title=Spezial:MathShowImage&hash=65e2d4ffe4d98015acbfcc03d766938f&mode=mathml) |
![{\displaystyle A\times B}](/index.php?title=Spezial:MathShowImage&hash=64e9a551eb59026062759b36637aedd3&mode=mathml) |
![{\displaystyle A\times C}](/index.php?title=Spezial:MathShowImage&hash=9c528535228e1cced48ad78ea8fa490d&mode=mathml) |
![{\displaystyle (A\times B)\cap (A\times C)}](/index.php?title=Spezial:MathShowImage&hash=ff742b0bd3e80a39e36bb29a55524391&mode=mathml) |
![{\displaystyle B\cap C}](/index.php?title=Spezial:MathShowImage&hash=bbb61f74fa0bac8be664f867abdf463b&mode=mathml) |
|
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
|
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \in }](/index.php?title=Spezial:MathShowImage&hash=986c22f151c46acac223b858e3fcf6fd&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
|
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \in }](/index.php?title=Spezial:MathShowImage&hash=986c22f151c46acac223b858e3fcf6fd&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
|
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \in }](/index.php?title=Spezial:MathShowImage&hash=986c22f151c46acac223b858e3fcf6fd&mode=mathml) |
![{\displaystyle \in }](/index.php?title=Spezial:MathShowImage&hash=986c22f151c46acac223b858e3fcf6fd&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \in }](/index.php?title=Spezial:MathShowImage&hash=986c22f151c46acac223b858e3fcf6fd&mode=mathml) |
|
![{\displaystyle \in }](/index.php?title=Spezial:MathShowImage&hash=986c22f151c46acac223b858e3fcf6fd&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
|
![{\displaystyle \in }](/index.php?title=Spezial:MathShowImage&hash=986c22f151c46acac223b858e3fcf6fd&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \in }](/index.php?title=Spezial:MathShowImage&hash=986c22f151c46acac223b858e3fcf6fd&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \in }](/index.php?title=Spezial:MathShowImage&hash=986c22f151c46acac223b858e3fcf6fd&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
|
![{\displaystyle \in }](/index.php?title=Spezial:MathShowImage&hash=986c22f151c46acac223b858e3fcf6fd&mode=mathml) |
![{\displaystyle \in }](/index.php?title=Spezial:MathShowImage&hash=986c22f151c46acac223b858e3fcf6fd&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \in }](/index.php?title=Spezial:MathShowImage&hash=986c22f151c46acac223b858e3fcf6fd&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
![{\displaystyle \notin }](/index.php?title=Spezial:MathShowImage&hash=37048599fef1997d666d579afe2d20f8&mode=mathml) |
|
![{\displaystyle \in }](/index.php?title=Spezial:MathShowImage&hash=986c22f151c46acac223b858e3fcf6fd&mode=mathml) |
![{\displaystyle \in }](/index.php?title=Spezial:MathShowImage&hash=986c22f151c46acac223b858e3fcf6fd&mode=mathml) |
![{\displaystyle \in }](/index.php?title=Spezial:MathShowImage&hash=986c22f151c46acac223b858e3fcf6fd&mode=mathml) |
![{\displaystyle \in }](/index.php?title=Spezial:MathShowImage&hash=986c22f151c46acac223b858e3fcf6fd&mode=mathml) |
![{\displaystyle \in }](/index.php?title=Spezial:MathShowImage&hash=986c22f151c46acac223b858e3fcf6fd&mode=mathml) |
![{\displaystyle \in }](/index.php?title=Spezial:MathShowImage&hash=986c22f151c46acac223b858e3fcf6fd&mode=mathml) |
![{\displaystyle \in }](/index.php?title=Spezial:MathShowImage&hash=986c22f151c46acac223b858e3fcf6fd&mode=mathml) |
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-->
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bla:
Geht leider nicht, da man ein Element x nimmt und schaut ob es in den Mengen enthalten ist. Bei AxB entsteht eine Menge von Tupel, da ist x nicht dabei. Blöd gelaufen - hat unser Tutor so bestätigt...
Die Elementetafel geht in der Form nicht, wegen des kartesischen Produkts.