If A = {a, b}, B = {2, 3, 5, 6, 7} and C = {5, 6, 7, 8, 9}, find A × (B ∩ C).

A
ϕ
{(5, a), (6, a), (7, a), (5, b), (6, b), (7, b)}
{(a, 5), (a, 6), (a, 7), (b, 5), (b, 6), (b, 7)}

Correct Answer: {(a, 5), (a, 6), (a, 7), (b, 5), (b, 6), (b, 7)}

Explanation:

We have,
(B ∩ C) = {2, 3, 5, 6, 7} ∩ {5, 6, 7, 8, 9}
= {5, 6, 7}
∴ A × (B ∩ C) = {a, b} × {5, 6, 7}
= {(a, 5), (a, 6), (a, 7), (b, 5), (b, 6), (b, 7)}.

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