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For any two sets A and B, prove the following: A – B = A Δ (A ∩ B) |
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Answer» = A Δ (A ∩ B) [∵ E Δ F =(E–F) ∪ (F–E) ] = (A–( A ∩ B)) ∪ (A ∩B –A) [∵ E – F = E ∩ F’] = (A ∩ (A ∩ B)’) ∪ (A∩B∩A’) = (A ∩ (A’∪B’)) ∪ (A∩A’∩B) = ϕ ∪ (A ∩ B’) ∪ ϕ = A ∩ B’ [∵A ∩ B’ = A–B] = A–B = LHS ∴ LHS = RHS Proved |
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