Question

Suppose n(X) = 28 and n(Y) = 19.

Answer 1

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

If $X$ and $Y$ share no common elements, then $n(X\cap Y)=0$, which means $n(X\cup Y)=n(X)+n(Y)=47$

On the other hand, if the smaller set is entirely contained within the larger set, i.e. $Y\subseteq X$, then $X\cap Y=Y$, and so $n(X\cup Y)=n(X)+n(Y)-n(Y)=n(X)=28$.