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If A and B are sets, then prove that A – B, A ∩ B and B – A are pair wise disjoint. |
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Answer» Let x ϵ A and y ϵ B A – B = The set of values of A that are not in B. A ∩ B = The set containing common values of A and B B – A = The set of values of B that are not in A. Two sets X and Y are called disjoint if, X ∩ Y = ϕ (A – B) ∩ (A ∩ B) = ((A – B) ∩ A) ∪ ((A – B) ∩B) (A – B) ∩ (A ∩ B) = ϕ ∪ ϕ (A – B) ∩ (A ∩ B) = ϕ Similarly, (B – A) ∩ (A ∩ B) = ((B – A) ∩ A) ∪ ((B – A) ∩B) (B – A) ∩ (A ∩ B) = ϕ Hence, the three sets are pair wise disjoint. |
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