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| 1. |
Show that for any sets A and B, A ∪ (B – A) = A ∪ B |
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Answer» Let x ϵ A ∪ (B – A) ⇒ x ϵ A or x ϵ (B–A) ⇒ X ϵ A or x ϵ B or x ∉ A ⇒ x ϵ A or x ϵ B ⇒ x ϵ (A ∪ B) ∴ A ∪ (B – A) ⊂ (A ∪ B)…….(1) Let and x ϵ (A ∪ B) ⇒ x ϵ A or x ϵ B ⇒ x ϵ A or x ϵ B and x ∉ A ⇒ x ϵ A or x ϵ B–A ⇒ x ϵ A ∪ (B–A) ∴ (A ∪ B) ⊂A ∪ (B – A)…….(2) From (1) and(2), we get A ∪ (B – A) = A ∪ B. |
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