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