Let X,Y,Z be sets. Prove that X union (Y intersecting Z) = (X union Y) intersecting (X union Z).

The proof would start off by showing that each side is a subset of the other, I believe... But there would be several cases? I'm not really sure where to go with this.. Any help would be wonderful.

2. Originally Posted by amm345
Let X,Y,Z be sets. Prove that X union (Y intersecting Z) = (X union Y) intersecting (X union Z).
From formal logic do you understand this
$p \vee \left( {q \wedge r} \right) \equiv \left( {p \vee q} \right) \wedge \left( {p \vee r} \right)$?

If not, then you need to do some background work in order to understand this question.

3. Yes, I understand this from the class, but each time I tried to do the proof I would end up with a contradiction.