Cardinality-wise, Is the amount of possible relations of x and y greater than or equal to the amount of possible functions of x?

Question

Consider the set of all possible relations of $x$ and $y$ (under Real Numbers) $S_{xy}$. The set of all possible functions of $x$, $S_x$, is therefore a subset of $S_{xy}$.

What is the cardinality of $S_{xy}$, $S_x$ and is $S_{xy}$ greater than $S_x$ or equal to it?

Answer 1

Number of relations = $2^{|X×Y|}.$
Number of functions = $|Y|^{|X|}.$

What is your conclusion?