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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 and x ϵ C} = {5, 6} A ∪ (B ∩ C) = {x: x ϵ A or x ϵ (B ∩ C) } = {1, 2, 4, 5, 6}. R.H.S = (A ∪ B) = {x: x ϵ A or x ϵ B } = {1, 2, 4, 5, 6}. (A ∪ C) = {x: x ϵ A or x ϵ C } = {1, 2, 4, 5, 6, 7}. (A ∪ B) ∩ (A ∪ C) = {x:x ϵ (A ∪ B) and x ϵ (A ∪ C) }. = {1, 2, 4, 5, 6}. Hence Verified. |
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