Question

If $n\left(A\right)=7,n\left(B\right)=5$ and $n(A\cup B)=10$, then find $n(A\cap B)$.

Answer 1

Given,

$n\left(A\right)=7,n\left(B\right)=5,n(A\cup B)=10$

Now,

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

$10=7+5-n(A\cap B)$

$n(A\cap B)=2$