Question

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

Answer 1

It is given that:
$n\left(X\right)=17,n\left(Y\right)=23,n(X\cup Y)=38$
$n(X\cap Y)=?$
Using the formula
$n(X\cup Y)=n\left(X\right)+n\left(Y\right)-n(X\cap Y)$
$\therefore 38=17+23-n(X\cap Y)$
$\Rightarrow n(X\cap Y)=40-38=2$
$\therefore n(X\cap Y)=2$