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Problem 81: (Additional Properties Of Cartesian Products)

Let $A$, $B$, $C$, and $D$ be sets. Prove or disprove each statement.

  1. $(A\times B)\cap(C\times D) = (A\cap C)\times(B\cap D)$
  2. $(A\times B)\cup(C\times D) = (A\cup C)\times(B\cup D)$

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