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**Aryth** I'm beginning a section on Product Topologies and I have to do a few problems, but I'm not seeing the difference between these two.

Let $\displaystyle \mathcal{A}$ and $\displaystyle \mathcal{B}$ be two nonempty families of sets. Prove that:

$\displaystyle \bigcap \mathcal{A} \times \bigcap \mathcal{B} = \bigcap\{A \times B : A \in \mathcal{A}, \ B \in \mathcal{B}\}$

Suppose that $\displaystyle A_1,\cdots ,A_n$ and $\displaystyle B_1,\cdots ,B_n$ are sets. Prove that:

$\displaystyle (A_1\times B_1)\cap\cdots\cap (A_n\times B_n) = (A_1\cap\cdots\cap A_n) \times (B_1\cap\cdots\cap B_n)$

Aren't these asking for the same thing??