Question

If $n\left(A\right)=3$ and $n\left(B\right)=6$ and $A\subseteq B$. Then the number of elements in $A\cap B$ is equal to

• A. $3$
• B. $9$
• C. $6$
• D. None of these.

Answer 1

The correct option is A

$3$

Explanation of the correct option

Given: $n\left(A\right)=3$ and $n\left(B\right)=6$ and $A\subseteq B$

Since $A\subseteq B$, it means all the terms of $A$ are present in $B$.

Thus $\left(A\cap B\right)=A$

$$\begin{gathered} \Rightarrow n(A\cap B)=n\left(A\right) \\ \Rightarrow n(A\cap B)=3 \end{gathered}$$

Therefore, number of elements in $\left(A\cap B\right)$ is $3$.

Hence, option(A) i.e. $3$ is the correct option.