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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 = C –  Daniel D C Oct 8 '12 at 12:27
    
No! It says nothing about $B$ and $C$ being subsets of $A$. There are no subset symbols in it whatsoever. –  Gerry Myerson Oct 8 '12 at 12:28
    
so i need to give a proof to state that is true –  Daniel D C Oct 8 '12 at 12:28
    
Daniel, look at the answer that has been posted. If you prove it's true, you will single-handedly destroy mathematics! –  Gerry Myerson Oct 8 '12 at 12:29
    
oh yeah whoops :| its been a long night –  Daniel D C Oct 8 '12 at 12:29
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marked as duplicate by Gerry Myerson, Martin Sleziak, Thomas, MJD, Norbert Oct 8 '12 at 18:14

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1 Answer

up vote 2 down vote accepted

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 answers.yahoo.com/question/index?qid=20101207140436AAMdBwv –  Daniel D C Oct 8 '12 at 12:33
    
In that link, they are trying to prove something. When you want to disprove something you have to find a counterexample. –  PAD Oct 8 '12 at 12:40
    
no worries thanks for your help –  Daniel D C Oct 8 '12 at 12:46
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