**apologies if this is the wrong part of the forum... it was the closest I could find **

Whilst doing questions in preparation for uni this year, I've been working on some abstract algebra. I was doing pretty well until I came across this:

$\displaystyle P=(A \cap B) \cup (C \cap D)$

$\displaystyle Q=(A \cup B) \cap (C \cup D)$

Prove that $\displaystyle P \subseteq Q$

It looks like it should be easy but it's been resisting all attempts that I've tried. I've tried a direct proof that $\displaystyle x \in P \Rightarrow x \in Q$ but that didn't go anywhere, nor did a contradiction.

Can anyone please make me look a fool and pull out a solution that is from THE BOOK?