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
$n\left(X\right)=40,n(X\cup Y)=60,n(X\cap Y)=10$
We know that:
$n(X\cup Y)=n\left(X\right)+n\left(Y\right)-n(X\cap Y)$
$\therefore 60=40++n\left(Y\right)-10$
$\therefore n\left(Y\right)=60-(40-10)=30$
Thus, the set Y has 30 elements.