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Let A = {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6}. Verify,(i) A × (B ∩ C) = (A × B) ∩ (A × C)(ii) A × (B ∪ C) = (A × B) ∪ (A × C) |
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Answer» A = {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6} (i) B ∩ C = {5, 6} A × (B ∩ C) = {(1, 5), (1, 6), (2, 5), (2, 6), (3, 5), (3, 6), (4, 5), (4, 6)} A × B = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6)} A × C = {(1, 5), (1, 6), (2, 5), (2, 6), (3, 5), (3, 6), (4, 5), (4, 6)} ∴ (A × B) ∩ (A × C) = {(1, 5), (1, 6), (2, 5), (2, 6), (3, 5), (3, 6), (4, 5), (4, 6)} ∴ A × (B ∩ C) = (A × B) ∩ (A × C) (ii) B ∪ C = {4, 5, 6} A × (B ∪ C)= {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3,4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6)} A × B = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6)} A × C = {(1, 5), (1, 6), (2, 5), (2, 6), (3, 5), (3, 6), (4, 5), (4, 6)} ∴ (A × B) ∪ (A × C) = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6)} ∴ A × (B ∪ C) = (A × B) ∪ (A × C) |
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