# Proving equalities with operations on sets

1. Jan 20, 2010

### King Tony

1. The problem statement, all variables and given/known data
Let A, B, C be any sets.

Prove that if $$C\subseteq A$$, then $$(A\cap B)\cup C$$ = $$A\cap (B\cup C)$$

2. Relevant equations

?

3. The attempt at a solution

Don't even know where to begin, If someone could point me in the right direction, that would be the best.

2. Jan 20, 2010

### vela

Staff Emeritus
To prove two sets A and B are equal, you need to show $A\subset B$ and $B\subset A$.

3. Jan 20, 2010

### King Tony

Thankyou! I think I'm on the right track, I see how that would make both sides equal only if C is a subset of A.