Question

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

Answer 1

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