Let A = {2, 3} and B = {4, 5}.
Question:

Let $A=\{2,3\}$ and $B=\{4,5\} .$ Find $(A \times B) .$ How many subsets will $(A \times B)$ have?

Solution:

Given: A = {2, 3} and B = {4, 5}

To find: A × B

By the definition of the Cartesian product,

Given two non – empty sets $P$ and $Q$. The Cartesian product $P \times Q$ is the set of all ordered pairs of elements from $P$ and $Q$, . i.e.

$P \times Q=\{(p, q): p \in P, q \in Q\}$

Here, $A=\{2,3\}$ and $B=\{4,5\}$. So,

$A \times B=(2,3) \times(4,5)$

$=\{(2,4),(2,5),(3,4),(3,5)\}$

$\therefore$ Number of elements of $A \times B=n=4$

Number of subsets of A × B = 2n

$=2^{4}$

= 2 × 2 × 2 × 2

$=16$

∴, the set A × B has 16 subsets.