Question:
For all sets A and B, (A ∪ B) – B = A – B
Solution:
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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