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

Find the value of intersection

Given,

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

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

$n(X\cup Y)=38$

We know that, by Venn Diagram for $2$ sets,

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

$\Rightarrow 38=17+23–n(X\cap Y)$

$\Rightarrow 38=40–n(X\cap Y)$

$\Rightarrow n(X\cap Y)=40-38$

$\Rightarrow n(X\cap Y)=2$

Hence, $n(X\cap Y)$ is $2$.