1.

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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