There's a very straight forward isomorphism between a set and it's indicator function. A relation \\(\triangle\\) is defined to be a subset of \\( S \times S\\). It's indicator function is then a function (\\(\chi)\\) from a pair of elements of S to a Boolean value (True or False) where \\[\chi (a,b) = True \iff a \triangle b \\]
So technically what we get is the indicator function of a relation. But the distinction is entirely unimportant in normal mathematical reasoning.