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If $A = \{a, b\}, B = \{c, d\}, C = \{d, e\},$ then
$\{(a, c), (a, d), (a, e) (b, c) (b, d), (b, e)\}$ is equal to

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$A \cap (B \cup C)$

$A \cup (B \cap C)$

$A \times (B \cup C)$

$A \times (B \cap C)$

answer is C.

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Detailed Solution

$B \cup C = \{c, d\} \cup \{d, e\} = \{c, d, e\}$

$∴ A \times (B \cup C) = \{a, b\} \times \{c, d, e\}$

$= \{(a, c), (a, d), (a, e), (b, c), (b, d), (b, e)\} .$

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