Originally Posted by

**p00ndawg** Prove or Give counter example:

$\displaystyle (AXB) \cap (CXD) = (A \cap C) X (B \cap D)$

kind of a long proof. But I was wondering if anyone could help check this for me.

I proved that $\displaystyle x \in A,C$ and $\displaystyle y \in B,D $. So $\displaystyle (AXB) \cap (CXD) $ was a subset of $\displaystyle (A \cap C) X (B \cap D)$.

When trying to prove that $\displaystyle (A \cap C) X (B \cap D)$ was a subset of $\displaystyle (AXB) \cap (CXD) $ I reached a contradiction, well what i believe was a contradiction. I found that

$\displaystyle x \in A$ and $\displaystyle x \in B$. Im just not sure if this is a contradiction or not. If its a contradiction, well im done, if it is not a contradiction I guess I would just continue on to prove it. Im just not sure if the last part of the proof is a contradiction.

Any help with this proof is greatly appreciated, and im sorry if this is somewhat unclear.