Answer is $D$.
As $X$ and $Y$ elements of $U$, $X$ and $Y$ are subsets of $S$.
Option $A$ is wrong consider $X=\{1,2\}$ therefore $X'=\{3,4,5,6\}$, $|X|=2$ and $|X'|=4$.
Option $B$ is wrong as any two possible subsets of $S$ with 5 elements should have atleast 4 elements in common (Pigeonhole principle). Hence, $X$ intersection $Y$ cannot be null.
Option $C$ is wrong, $X$ and $Y$ can have any number of elements from $0$ to $5$. Even for the given constraint, consider $X=\{1,2\}, Y=\{3,4,5\}$ and $X\backslash Y=\{1,2\}$ which is not null.