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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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    I deleted some comme$n$ts 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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    no worries thanks for your help2012-10-08