Question

If $n\left(\xi \right)$ $=30,n\left(A\right)=22,n\left(B\right)=15$ and $n(A$ $\cup$ $B)=25$, then find : $n(A$ $\cap$ $B$ ${}^{{}^{\prime }}$ $)$

Answer 1

Using the formula, $n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$

So, $n(A\cap B)=n\left(A\right)+n\left(B\right)-n(A\cup B)=22+15-25=12$

And $n\left({A\cap B}^{{}^{\prime }}\right)=n\left(\xi \right)-n(A\cap B)=30-12=18$