Question

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

Answer 1

Here

n(X) = 17, n(Y) = 23

and $n(X\cup Y)=38,$

We know that

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

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

$\therefore$ $n(X\cap Y)=40-38=2.$