About this document Functions and equivalence relations 2.1.1. Let S and T be sets. The set S is called the domain of the function, and the set T is called the codomain of the function.
Composition of functions is associative.
Suppose that S and T are finite sets with the same number of elements. Let S be a set. Let S be a set. Let be an equivalence relation on the set S. For a given element a S, we define the equivalence class of a to be the set of all elements of S that are equivalent to a. Then each element of S belongs to exactly one of the equivalence classes of S determined by the relation .