Question

Let $A=\left\{1,2\right\}$, $B=\left\{3,4\right\}$. Then, the number of subsets of $A\times B$ is

• A. $4$
• B. $8$
• C. $18$
• D. $16$

Answer 1

The correct option is D

$16$

Explanation for correct option:

Finding $n(A\times B)$:

Given $A=\left\{1,2\right\}$, $B=\left\{3,4\right\}$

$$\begin{gathered} A\times B=\left\{\left(1,3\right),\left(1,4\right),\left(2,3\right),\left\{2,4\right\}\right\} \\ \Rightarrow n(A\times B)=4 \end{gathered}$$

If $A$is a set, then the set of all subsets of $A$ is called the power set of $A$and is usually denoted as $P\left(A\right)$. The number of elements in $P\left(A\right)$ is $2^n$.

Number of subsets of $A\times B=2^4=16$
Hence, option (D) is the correct answer.