Question

If $X$ and $Y$ are two sets such that $X\cup Y$ has $50$ elements, $X$ has $28$ elements and $Y$ has $32$ elements, how many elements does $X\cap Y$ have?

Answer 1

Given data : $n(X\cup Y)=50,n\left(X\right)=28,n\left(Y\right)=32$
We have to solve for $X\cap Y$
$\because n(X\cup Y)=n\left(X\right)+n\left(Y\right)-n(X\cap Y)$
$\Rightarrow 50=28+32-n(X\cap Y)$
$\Rightarrow n(X\cap Y)=28+32-50$
$\Rightarrow n(X\cap Y)=60-50$
$\Rightarrow n(X\cap Y)=10$