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Question
Show that for any sets A and B, A ∪ (B – A) = (A ∪ B)
Solution
Left side = A ∪ (B – A)
= A ∪ (B ∩ A’) [∴ B – A = B ∩ A’]
= (A ∪ B) ∩ (A ∪ A') (by distributive law)
= (A ∪ B) ∩ U [Here U is the universal set]
= A ∪ B
Hence, A ∪ (B – A) = A ∪ B.
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