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.

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- Feb 18th 2013, 11:59 PMzachoonProof involving sets, crossproducts, and intersections
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. - Feb 19th 2013, 12:36 AMSironRe: Proof involving sets, crossproducts, and intersections
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 ...