InterviewSolution
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Show that for any sets A and B, A = (A ∩ B) ∩ (A – B) |
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Answer» We know that (A ∩ B) ⊂ A and (A – B) ⊂ A ⇒(A ∩ B) ∩ (A – B)⊂ A….(1) Let and x ϵ (A ∩ B) ∩ (A – B) ⇒ x ϵ (A ∩ B) and x ϵ (A–B) ⇒ x ϵ A and x ϵ B and x ϵ A and x ∉ B ⇒ x ϵ A and x ϵ A [∵ x ϵ B and x ∉ B are not possible simultaneously] → x ϵ A ∴ (A ∩ B) ∩ (A – B)⊂ A…(2) From (1) and (2), we get A = (A ∩ B) ∩ (A – B) |
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