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Question
For all sets A and B, A ∪ (B – A) = A ∪ B
Solution
There are two sets A and B
To prove: A ∪ (B – A) = A ∪ B
Take L.H.S
A ∪ (B – A)
= A ∪ (B ∩ A’) .....[∵ A – B = A ∩ B’]
= (A ∪ B) ∩ (A ∪ A’)
∵ Distributive property of set:
(A ∪ B) ∩ (A ∪ C) = A ∪ (B ∩ C)}
= (A ∪ B) ∩ U .....[∵ A ∪ A’ = U]
= A ∪ B
= R.H.S
Hence Proved
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