Q18 of 58 Page 12

Using properties of sets prove the statements given

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

Given: 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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