(b) 2 and 3
1. A – (B ∪ C) = (A – B) ∪ (A – C)
(A – B) ∪ (A – C)
⇒ For all (x ∈ A and x ∉ B) or (x ∈ A and x ∉ C)
⇒ For all (x ∈ A and x ∉ B and x ∉ C)
⇒ x ∈ A – (B ∩ C )
Hence not correct.
2. x ∈ (A – (A ∩ B)) ⇒ x ∈ A and x ∉ A ∩ B
⇒ x ∈ A and x ∉ B
⇒ x ∈ (A – B)
3. x ∈ [(A ∩ B) ∪ (A – B)]
⇒ (x ∈ A and x ∉ B) or (x ∈ A and x ∈ B′)
⇒ x ∈ A and x ∈ B and x ∈ B′
⇒ x ∈ A and x ∈ B ∩ B′
⇒ x ∈ A and x ∈ ϕ
⇒ x ∈ A ∪ ϕ
⇒ x ∈ A
Hence (1) is incorrect.