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1. |
For any sets A and B show that (i) (A ∩ B) ∪ (A – B) = A (ii) A ∪ (B - A) = A ∪ B |
Answer» (i) (A ∩ B) ∪ (A – B) = A L.H.S = (A ∩ B) ∪ (A – B) = (A ∩ B) ∪ (A – B’) [∴ (A – B) = (A – B’] = A ∩ (B ∪ B’) [By distributive law] = A ∩ (U) [(B υ B') = U =Universal set] = A = R.H.S (ii) A ∪ (B - A) = A ∪ B L.H.S = A ∪ (B - A) = A ∪ (B – A’) [∴ (B - A) = (B ∩ A’] = (A ∪ B) ∩ (A ∪ A’) [By distributive law] = (A ∪ B) ∩ U = A ∪ B [∴ A υ A' = U =Universal set] = R.H.S |
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