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If A = {x : x ϵ N, x ≤ 7}, B = {x : x is prime, x < 8} and C = {x : x ϵ N, x is odd and x < 10}, verify that: (i) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) (ii) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) |
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Answer» : Natural numbers start from 1 A = {1, 2, 3, 4, 5, 6, 7} B = {2, 3, 5, 7} C = {1, 3, 5, 7, 9} (i) B∩C = {3, 5, 7} AU(B∩C) = {1, 2, 3, 4, 5, 6, 7} A∪B = {1, 2, 3, 4, 5, 6, 7} A∪C = {1, 2, 3, 4, 5, 6, 7, 9} (A∪B)∩(A∪C) = {1, 23, 4, 5, 6, 7} A∪(B∩C) = (A∪B)∩(A∪C) Hence proved (ii) B∪C = {1, 2, 3, 5, 7, 9} A∩(B∪C) = {1, 2, 3, 5, 7} A∩B = {2, 3, 5, 7} A∩C = {1, 3, 5, 7} (A∩B)∪(A∩C) = {1, 2, 3, 5, 7} A∩(B∪C) = (A∩B)∪(A∩C) |
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