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If A = {1, 2, 3}, B = {2, 3, 4}, C = {1, 3, 4} and D = {2, 4, 5}, then (A × B) ∩ (C × D) = ?
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- (A ∩ D) × (B ∩ C)
- (b) (A ∩ C) × (B ∩ D)
- ϕ
- None of these
Correct Option: B
(A × B) = {1, 2, 3} × {2, 3, 4}
= {(1, 2), (1, 3), (1, 4), (2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)}
(C × D) = {1, 3, 4} × {2, 4, 5}
= {(1, 2), (1, 4), (1, 5), (3, 2), (3, 4), (3, 5), (4, 2), (4, 4), (4, 5)}
∴ (A ∩ B) ∩ (C × D)
= {(1, 2), (1, 4), (3, 2), (3, 4)}
Also, (A ∩ C) = {1, 3} and (B ∩ D) = {2, 4}. Therefore,
(A ∩ C) × (B ∩ D) = {(1, 2), (1, 4), (3, 2), (3, 4)}
Hence, (A × B) ∩ (C × D) = (A ∩ C) × (B ∩ D).
