Question

If $A\subset B,n\left(A\right)=5$ and $n\left(B\right)=7$, then $n(A\cup B)=$ ______

• A. $5$
• B. $7$
• C. $2$
• D. $12$

Answer 1

Answer: (B)

$7$

Given $A\subset B$, $n\left(A\right)=5$ and $n\left(B\right)=7$

Since, $A\subset B\Rightarrow$ all the elements of set $A$ are also present in set $B$ $\Rightarrow n(A\cap B)=5$

Since, $n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$

$\Rightarrow n(A\cup B)=5+7-5$

$\Rightarrow n(A\cup B)=7$

Option $B$ is correct.