Proving equalities with operations on sets

[King Tony]

Homework Statement

Let A, B, C be any sets.

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

Homework Equations

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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.

 

[vela]

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

 

[King Tony]

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

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.