Question

If $n\left(U\right)=60,n\left(A\right)=35,n\left(B\right)=24$ and $n{\left(A\cup B\right)}^{\prime }=10$ then $n\left(A\cap B\right)$ is

• A. 9
• B. 8
• C. 6
• D. 7

Answer 1

The correct option is A 9

We have $n(A\cup B)=n\left(U\right)-n{(A\cup B)}^{\prime }$

$\Rightarrow n(A\cup B)=60-10=50$ from the question

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

$n(A\cap B)=35+24-50=59-50=9$ from the question

$\therefore n(A\cap B)=9$