Is it 16 (2^4)?
I completely forgot how to calculate the number of relations on a given set.
Is it 16 (2^4)?
I completely forgot how to calculate the number of relations on a given set.
If you mean $S = \{a, b\}$, a set with $2$ elements, then a relation is simply an element of the powerset of $S^2$. So your answer is correct.
Suppose $X$ is a set of $n$ elements. Then for any ordered pair $(x,y)$ of elements of $X$, we can say Yes or No to the question of whether $(x,y)$ is in the (binary) relation on $X$. There are $2^{n^2}$ ways to make the choices, and therefore $2^{n^2}$ binary relations on $X$.
If $X$ is the $2$-element set $\{a,b\}$, the number of relations on $X$ is therefore $2^{(2^2)}$.