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Possible Duplicate:
Subsets and equality

Hello I'm new to set theory and I want to know how I can solve the following question

Let $U$ be a universe and $A,B$ and $C$ be subsets of $U$. Prove or disprove:

$$(A \cup B) = (A \cup C)\implies B = C$$

(question also found here)

I'm looking at the "Typical element" Method of proving this statement but I'm confused on how to go about it or if it is even the correct method to be using.

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    ok that makes much more sense to me now! so its saying if B and C are subsets of A then B = C2012-10-08
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    No! It says nothing about $B$ and $C$ being subsets of $A$. There are no subset symbols in it whatsoever.2012-10-08
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    so i need to give a proof to state that is true2012-10-08
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    Daniel, look at the answer that has been posted. If you prove it's true, you will single-handedly destroy mathematics!2012-10-08
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    oh yeah whoops :| its been a long night2012-10-08
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    Night? You in Australia?2012-10-08
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    ok i need to prove that its wrong then2012-10-08
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    yea in Australia2012-10-08
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    I deleted some comments discussing the correct notations to use in the question statement, which have resulted in appropriate changes in the question and hence are now obsolete.2012-10-08

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Take $A=\{1,2 \}$, $B=\{1 \}$, $C=\{2 \}$. No relation between $B$, $C$.

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    i think im more after this kind of answer http://answers.yahoo.com/question/index?qid=20101207140436AAMdBwv2012-10-08
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    In that link, they are trying to prove something. When you want to disprove something you have to find a counterexample.2012-10-08
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    no worries thanks for your help2012-10-08