# Entry Level Set Theory Proof [duplicate]

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:

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

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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## marked as duplicate by Gerry Myerson, Martin Sleziak, Thomas, MJD, NorbertOct 8 '12 at 18:14

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

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