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

Given data: $n\left(X\right)=17,n\left(Y\right)=23,n(X\cup Y)=38$
Solve for $n(X\cap Y)$
We know that
$n(X\cup Y)=n\left(X\right)+n\left(Y\right)-n(X\cap Y)$
$\Rightarrow 38=17+23-n(X\cap Y)$
$\Rightarrow 38=40-n(X\cap Y)$
$\Rightarrow n(X\cap Y)=40-38$
$\Rightarrow n(X\cap Y)=2$

Final answer:
$n(X\cap Y)=2$