Question

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

• A. $9$
• B. $8$
• C. $6$
• D. $7$

Answer 1

The correct option is A $9$

we have formula,

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

$n(A\cup B)=60-10=50$

Now,

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

$50=35+24-n(A\cap B)$

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