I have this problem, i'm not quite sure how to go about proving it. If anyone could point something helpful out or ideas, that would be great.
Prove: (AxB)∩(CxD)=(A∩C)x(B∩D)
Thanks.
Prove two inclusions.
1. $\displaystyle (A \times B) \cap (C \times D) \subset (A \cap C) \times (B \cap D)$
Let $\displaystyle x \in (A \times B) \cap (C \times D)$ then $\displaystyle x \in A \times B \wedge x \in C \times D$. Let $\displaystyle x=(u,v)$ then we have $\displaystyle (u,v) \in A \times B \wedge (u,v) \in C \times D$, thus $\displaystyle u \in A \cap C$ and $\displaystyle v \in B \cap D$. Hence $\displaystyle x = (u,v) \in (A \cap C) \times (B \cap D)$.
2. Prove the other inclusion ...