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

(N/A) To verify: $A \times C$ is a subset of $B \times D$.
First,calculate the Cartesian product $A \times C$:
$A \times C = \{(1, 5), (1, 6), (2, 5), (2, 6)\}$.
Next,calculate the Cartesian product $B \times D$:
$B \times D = \{(1, 5), (1, 6), (1, 7), (1, 8), (2, 5), (2, 6), (2, 7), (2, 8), (3, 5), (3, 6), (3, 7), (3, 8), (4, 5), (4, 6), (4, 7), (4, 8)\}$.
We observe that every element of $A \times C$ is present in $B \times D$.
Therefore,$A \times C \subset B \times D$ is verified.