Let $A = \{1, 2, 3\}$,$B = \{3, 4\}$ and $C = \{4, 5, 6\}$. Find $(A \times B) \cup (A \times C)$.

(D) First,we find the Cartesian products $A \times B$ and $A \times C$:
$A \times B = \{(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)\}$
$A \times C = \{(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)\}$
Now,we find the union $(A \times B) \cup (A \times C)$ by combining all unique ordered pairs from both sets:
$(A \times B) \cup (A \times C) = \{(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6)\}$