Let $A$, $B$, $C$ be sets. Show that $A \times (B \cup C) = (A \times B) \cup (A \times C)$, that $A \times (B \cap C) = (A \times B) \cap (A \times C)$, and that $A \times (B \setminus C) = (A \times B) \setminus (A \times C)$. (One can of course prove similar identities in which the rôles of the left and right factors of the Cartesian product are reversed.)

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Analysis I

Exercise 3.5.4 (Cartesian products and set unions, set intersections and set differences)

Let $A$ , $B$ , $C$ be sets. Show that $A \times (B \cup C) = (A \times B) \cup (A \times C)$ , that $A \times (B \cap C) = (A \times B) \cap (A \times C)$ , and that $A \times (B ∖ C) = (A \times B) ∖ (A \times C)$ . (One can of course prove similar identities in which the rôles of the left and right factors of the Cartesian product are reversed.)

Exercise 3.5.4 (Cartesian products and set unions, set intersections and set differences)

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