Random Mathematics - Sets Relations And Functions Practice

Let $A = \{1, 2\}$, $B = \{1, 2, 3, 4\}$, $C = \{5, 6\}$ and $D = \{5, 6, 7, 8\}$. Verify that
(i) $A \times (B \cap C) = (A \times B) \cap (A \times C)$.
(ii) $A \times C$ is a subset of $B \times D$.