defining two sets: A = {a, b} and B = {5, 6}. Both set A and set B consist of two elements each. Their Cartesian product, written as A × B, results in a new set which has the following elements: A × B = {(a,5), (a,6), (b,5), (b,6)}.

Suppose A is a set and R is an equivalence relation on A. For each elementain A, the equivalence class of a,[a], is the set of allelementxinAsuch thatxis related toabyR:[a] =fxjx2Aand(x,a)2Rg