Question

If A and B are two sets such that $n\left(A\right)=27,n\left(B\right)=35$ and $n(A\cup B)=50,$ find $n(A\cap B)$

Answer 1

$n\left(A\right)=27,n\left(B\right)=35,n(A\cup B)=50,n(A\cap B)=?$
$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$
$50=27+35-n(A\cap B)$
$n(A\cap B)=62-50$
$\therefore (A\cap B)=12$