Question

If $X$ and $Y$ are two sets such that $n\left(X\right)=17$,$n\left(Y\right)=23$ $n(X\cup Y)=38$ find $n(X\cap Y)$

Answer 1

$n\left(X\right)=17$

$n\left(Y\right)=23$

$n(X\cup Y)=38$

$n(X\cap Y)=n\left(X\right)+n\left(Y\right)-n(X\cup Y)$

$n(X\cap Y)=17+23-38=2$

$n(X\cap Y)=2$