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Using properties of sets prove the given statement.For all sets A and B, A ∪ (B – A) = A ∪ B |
Answer» According to the question, There are two sets A and B To prove: A ∪ (B – A) = A ∪ B L.H.S = A ∪ (B – A) Since, A – B = A ∩ B’, we get, = A ∪ (B ∩ A’) Since, distributive property of set ⇒ (A ∪ B) ∩ (A ∪ C) = A ∪ (B ∩ C), we get, = (A ∪ B) ∩ (A ∪ A’) Since, A ∪ A’ = U, we get, = (A ∪ B) ∩ U = A ∪ B = R.H.S Hence Proved |
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