Let $A = \{1, 2\}$ and $B = \{3, 4\}$. Find $A \times B$. How many subsets will $A \times B$ have? List them.

Given $A = \{1, 2\}$ and $B = \{3, 4\}$.
$A \times B = \{(1, 3), (1, 4), (2, 3), (2, 4)\}$.
The number of elements in $A \times B$ is $n(A \times B) = 4$.
The number of subsets of a set with $m$ elements is $2^m$.
Therefore,the number of subsets of $A \times B$ is $2^4 = 16$.
The subsets are:
$\varnothing, \{(1, 3)\}, \{(1, 4)\}, \{(2, 3)\}, \{(2, 4)\}, \{(1, 3), (1, 4)\}, \{(1, 3), (2, 3)\}, \{(1, 3), (2, 4)\}, \{(1, 4), (2, 3)\}, \{(1, 4), (2, 4)\}, \{(2, 3), (2, 4)\}, \{(1, 3), (1, 4), (2, 3)\}, \{(1, 3), (1, 4), (2, 4)\}, \{(1, 3), (2, 3), (2, 4)\}, \{(1, 4), (2, 3), (2, 4)\}, \{(1, 3), (1, 4), (2, 3), (2, 4)\}$.