Question

If $n\left(A\right)=115$, $n\left(B\right)=326$, $n(A-B)=47$ then $n(A\cup B)$ is equal to

• A. $373$
• B. $165$
• C. $370$
• D. None

Answer 1

The correct option is A $373$

$n\left(A\right)=115,n\left(B\right)=326$

$n(A-B)=47$

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

$n(A\cap B)=n\left(A\right)-n(A-B)$

$\therefore n(A\cap B)=115-47=68$

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

$\Rightarrow n(A\cup B)=115+326-68$

$\Rightarrow n(A\cup B)=373$