Question

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

Answer 1

We know that

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

$\Rightarrow n(A\cap B)=n\left(A\right)+n\left(B\right)-n(A\cup B)=(27+35-50)=12$

Hence, $n(A\cap B)=12$