Given: A, B, C and D are four sets such that A ∩ B = C ∩ D = ϕ Statement 1: A ∪ C and B ∪ D are always disjoint. ⇒ (A ∪ C) ∩ (B ∪ D) = [(A ∪ C) ∩ B] ∪ [(A ∪ C) ∩ D] = [(A ∩ B) ∪ (C ∩ B)] ∪ [(A ∩ D) ∪ (C ∩ D)] = [ϕ ∪ (C ∩ B)] ∪ [(A ∩ D) ∪ ϕ] = (C ∩ B)] ∪ [(A ∩ D) (∵ A ∪ ϕ = A) (A ∪ C) and (B ∪ D) is not disjoint set. Statement 2: A ∩ C and B ∩ D are always disjoint. ⇒ (A ∩ C) ∩ (B ∩ D) = [(A ∩ C) ∩ B] ∩ [(A ∩ C) ∩ D] = [(A ∩ B) ∩ C] ∩ [(A ∩ (C ∩ D)] = [ϕ ∩ C] ∩ [(A ∩ ϕ] (∵ A ∩ ϕ = ϕ) = (ϕ ∩ ϕ) = ϕ (A ∩ C) and (B ∩ D) are always disjoint. Hence statement 2 is correct.