Q21 of 58 Page 12

Using properties of sets prove the statements given

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

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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Let A, B and C be sets. Then show that

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