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Let A = {a, b, c}, B = {b, c, d, e} and = {c, d, e, f} be subsets of U = {a, b, c, d, e, f}. Then verify that: (i) (A’)’ = A (ii) (A ∪ B)’ = (A’ ∩ B’) (iii) (A ∩ B)’ = (A’ ∪ B’) |
Answer» (i) A’ = {d, e, f} (A’)’ = {a, b, c} = A Hence proved (ii) A∪B = {a, b, c, d, e} (A∪B)’ = {f} A’ = {d, e, f} B’ = {a, f} A’∩B’ = {f} (A∪B)’ = (A’∩B’) Hence proved (iii) A’∪B’ = {a, d, e, f} A∩B = (b, c} (A∩B)’ = {a, d, e, f} (A∩B)’ = A’∪B’ Hence proved |
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