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

Here

$n\left(X\right)=40,n(X\cup Y)=60$

and $n(X\cap Y)=10$

We know that

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

$60=40+n\left(Y\right)-10$

$\therefore n\left(Y\right)=60-30=30.$