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Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the following identities: A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) |
Answer» L.H.S. (B ∪ C) = {x: x ϵ B or x ϵ C } = {2, 3, 4, 5, 6, 7}. (A ∩ (B ∪ C)) = {x:x ϵ A and x ϵ (B ∪ C)} = {2, 4, 5} R.H.S: (A ∩ B) = {x:x ϵ A and x ϵ B} = {2, 5} (A ∩ C) = {x:x ϵ A and x ϵ C} = {4, 5} (A ∩ B) ∪ (A ∩ C) = {x:x ϵ (A∩B) and x ϵ (A∩C) }. = {2, 4, 5}. Hence verified |
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