Given, A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6}, D = {5, 6, 7, 8} (i) B ∩ C = ϕ ∴ A × (B ∩ C) = A × ϕ = ϕ ...(1) A × B = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4)} A × C = {(1, 5), (1, 6), (2, 5), (2, 6)} ∴ (A × B) ∩ (A × C) = ϕ ...(2) From (1) & (2), we get A × (B ∩ C) = (A × B) ∩ (A × C). (ii) A × C = {(1, 5), (1, 6), (2, 5), (2, 6)} B × D = {(1, 5), (1, 6), (1, 7), (1, 8), (2, 5), (2, 6), (2, 7), (2, 8), (3, 5), (3, 6), (3, 7), (3, 8), (4, 5), (4, 6), (4, 7), (4, 8)} As every element of A × C is contained in B × D. ∴ (A × C) ⊂ (B × D) i.e., A × C is a subset of B × D.