Homework Help: 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.