A relation on a set S is a subset R of S x S. In other words, a relation R consists of a set of ordered pairs of the form (a,b) where a and b are in S. A partition of a set consists of a collection...A relation on a set S is a subset R of S x S. In other words, a relation R consists of a set of ordered pairs of the form (a,b) where a and b are in S. A partition of a set consists of a collection of non-empty subsets of A that are mutually disjoint and have union equal to A. An equivalence relation on a set A serves to partition A by the equivalence classes.