Question

For any two sets $A\&B;n\left(A\right)=4,n\left(B\right)=7,n\left(A\Delta B\right)=3$, then, $n(A\cap B)=$

Answer 1

Given $n\left(A\right)=4,n\left(B\right)=7,n\left(A\Delta B\right)=3$
We know the formula, i.e.,
$n\left(A\Delta B\right)=n\left(A\right)+n\left(B\right)-2n(A\cap B)$.
$\Rightarrow 3=4+7-2n(A\cap B)$
$\Rightarrow n(A\cap B)=\frac{4+7-3}{2}=4.$