Question

If A and B are two sets such that $n\left(A\cup B\right)=50,n\left(A\right)=28\mathrm{and}n\left(B\right)=32$, find $n\left(A\cap B\right)$.

Answer 1

We know:
$$\begin{gathered} n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B) \\ \Rightarrow 50=28+32-n(A\cap B) \\ \Rightarrow n(A\cap B)=60-50=10 \end{gathered}$$