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Let A = {1,2,4,5}, B = {2,3,5,6}, C = {4,5,6,7} verify the following identity A ∪ (B∩C) = [(A ∪ B) ∩ (A ∪ C)] |
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Answer» L.H.S = A ∪ (B ∪ C) = {1,2,3,4,5} ∪ [{2,3,5,6} ∩ {4,5,6,7}] = {1,2,4,5} ∪ {5,6} = {1,2,4,5,6} R.H.S = (A ∪ B) ∩ (A ∪ C) = [{1,2,4,5} ∪ {2,3,5,6}] ∩ [{1,2,4,5} ∪ {4,5,6,7}] = {1,2,3,4,5,6} ∩ {1,2,4,5,6,7} = {1,2,4,5,6} ∴ L.H.S = R.H.S |
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