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