Question

If A and B are two sets such that $n\left(A\right)=115,n\left(B\right)=326,n\left(A-B\right)=47,$ then write $n\left(A\cup B\right)$.

Answer 1

$$\begin{gathered} n\left(A\right)=115,n\left(B\right)=326andn\left(A-B\right)=47 \\ Now, \\ n\left(A\right)-n\left(A\cap B\right)=n\left(A-B\right) \\ \Rightarrow 115-n\left(A\cap B\right)=47 \\ \Rightarrow n\left(A\cap B\right)=68 \end{gathered}$$
Thus, we get:
$n\left(A\cup B\right)=n\left(A\right)+n\left(B\right)-n\left(A\cap B\right)$
= 115 + 326 $-$ 68
= 373