Question

If $X$ and $Y$ are two sets such that $X$ has $40$ elements, $X\cup Y$ has $60$ elements and $X\cap Y$ has $10$ elements, how many elements does $Y$ have?

Answer 1

Given data:
$n\left(X\right)=40,n(X\cup Y)=60,n(X\cap Y)=10$

Solve for $n\left(Y\right)$
We know that,
$n(X\cup Y)=n\left(X\right)+n\left(Y\right)-n(X\cap Y)$
$\Rightarrow 60=40+n\left(Y\right)-10$
$\Rightarrow 60=n\left(Y\right)+30$
$\Rightarrow n\left(Y\right)=60-30$
$\Rightarrow n\left(Y\right)=30$

Final answer:
The set $Y$ has $30$ elements.