Equivalence relation is a binary relation on nonempty set a. If R is reflexive, symmetric and transitive, it is said that R is an equivalence relation on A ... Given a nonempty set A, if there is a set s = {s, s, ..., s}, where s a, s (I = 1, 2, ..., m) and S S = (i j).

The purpose of studying equivalence relation is to classify the elements in the set and select the representative elements of each category to reduce the complexity of the problem. For example, in software testing, equivalence classes can be used to select test cases.

Extended data:

definition

If the relation R is reflexive, symmetric and transitive in the set A, it is called an equivalent relation on A. Is the relation R a Cartesian product? A subset of a× a.

The two elements X and Y in A have a relation R. If (X, y) ∈ R, we often abbreviate it as xRy.

Reflexive: If any X belongs to A, then X is related to itself, that is, xRx；;

Symmetry: Any X and Y belong to A. If X and Y have a relationship R, that is, xRy, then Y and X also have a relationship R, that is, yRx；;

Transfer: any x, y and z belong to a, if xRy and yRz, then xRz.

If x and y have equivalence relation r, they are said to be equivalent, sometimes called equivalence.