Question

If A and B are two sets such that $n\left(A\right)=20,n\left(B\right)=25$ and $n\left(A\cup B\right)=40$, then write $n\left(A\cap B\right)$.

Answer 1

We have:
$n\left(A\right)=20,n\left(B\right)=25andn\left(A\cup B\right)=40$
We know:
$$\begin{gathered} n\left(A\cup B\right)=n\left(A\right)+n\left(B\right)-n\left(A\cap B\right) \\ \Rightarrow n\left(A\cap B\right)=n\left(A\right)+n\left(B\right)-n\left(A\cup B\right) \end{gathered}$$
= 20 + 25 $-$ 40
= 5