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If A = { 1, 2, 3}, B = {1, 2} and C = {2, 3}, which one of the following is correct?(a) (A × B) ∩ (B × A) = (A × C) ∩ (B × C) (b) (A × B) ∩ (B × A) = (C × A) ∩ (C × B) (c) (A × B) ∪ (B × A) = (A × B) ∪ (B × C) (d) (A × B) ∪ (B × A) = (A × B) ∪ (A × C) |
Answer» (c) (A × B) ∪ (B × A) = (A × B) ∪ (B × C) (A × B) = { (1,1), (1,2), (2,1), (2,2), (3,1), (3,2)} (B × A) = { (1,1), (1,2), (1,3), (2,1), (2,2), (2,3)} (B × C) = { (1,2), (1,3), (2,2), (2,3)} (C × B) = { (2,1), (2,2), (3,1), (3,2)} (A × C) = { (1,2), (1,3), (2,2), (2,3), (3,2) (3,3)} (C × A) = { (2,1), (2,2), (2,3), (3,1), (3,2) (3,3)} ∴ (A × B) ∪ (B × A) = {(1,1), (1,2), (2,1), (2,2), (3,1), (3,2) (1,3), (2,3)} and (A × B) ∪ (B × C) = { (1,1), (1,2), (2,1), (2,2), (3,1), (3,2), (1,3), (2,3)} ∴ (A × B) ∪ (B × A) = (A × B) ∪ (B × C) |
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