Question

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

• A. $373$
• B. $165$
• C. $370$
• D. $394$

Answer 1

The correct option is A

$373$

Explanation of the correct option

We know that, for two sets $A$ and $B$.

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

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

Given: $n\left(A\right)=115,n\left(B\right)=326,n(A-B)=47$.

So, $47=115-n\left(A\cap B\right)$

$\Rightarrow$$n(A\cap B)=68$

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

$$\begin{gathered} \Rightarrow n\left(A\cup B\right)=115+326-68 \\ \Rightarrow n\left(A\cup B\right)=373 \end{gathered}$$

Therefore, $n(A\cup B)$ is equal to $373$.

Hence, option(A) i.e. $373$ is the correct option.