Question

If $n\left(\xi \right)$ $=200,n\left(A\right)=80,n\left(C\right)=50$ and $n(A$ $\cap$ $C)=30$, then find: $n(A$ $\cup$ B)${}^{{}^{\prime }}$ $-n\left(C\right)$.

Answer 1

Using the formula,
$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$

$n(A\cup B)=80+75-30=125$
And $n(A\cup B){}^{\prime }=\xi -n(A\cup B)=200-125=75$
Thus, $n(A\cup B){}^{\prime }-n\left(C\right)=75-50=25$