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.