(i) (A ∩ B) ∪ (A – B) = A
L.H.S = (A ∩ B) ∪ (A – B)
= (A ∩ B) ∪ (A – B’) [∴ (A – B) = (A – B’]
= A ∩ (B ∪ B’) [By distributive law]
= A ∩ (U) [(B υ B') = U =Universal set]
= A
= R.H.S
(ii) A ∪ (B - A) = A ∪ B
L.H.S = A ∪ (B - A)
= A ∪ (B – A’) [∴ (B - A) = (B ∩ A’]
= (A ∪ B) ∩ (A ∪ A’) [By distributive law]
= (A ∪ B) ∩ U
= A ∪ B [∴ A υ A' = U =Universal set]
= R.H.S
