Closure of a relation R is the smallest relation containing R and meeting a property EG. reflexive closure of R (on A) is R | { (a, a) | a \in A } symmetric closure of R is R | mirror(R) Equivalent: R is reflexive, symmetric, and transitive - f(x) = f(y) for some function f Equivalence classes: sets of values which R considers equivalent disjoint, nonempty subsets of domain