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For any two sets A and B, prove the following: A – (A – B) = A ∩ B |
Answer» For any sets A and B we have De morgans law (A ∪B)’ =A’ ∩B’ , (A ∩ B)’ = A’ ∪ B’ =A – (A–B) = A ∩ (A–B)’ = A∩(A∩B’)’ = A∩(A’∪ B’)’) = A ∩ (A’∪B) = (A ∩ A’) ∪ (A ∩ B) = ϕ ∪ (A ∩ B) = (A ∩ B) |
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