Question

If A and B are two sets such that $n\left(A\cup B\right)=50$, n(A) = 28 and n(B) = 32, find $n\left(A\cap B\right)$.

Answer 1

$n(A\cup B)=50$

$n\left(A\right)=28$

$n\left(B\right)=32$

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

$=28+32-50$

$=60-50$

$=10$

So, $n(A\cap B)=10$.