Let a nonempty set s and its binary relation ~ satisfy:

(1) reflexivity: a ~ a

(2) symmetry: A~B, then B ~ A；;

(3) transitivity: A~B, B~C, and then a ~ C.

Then ~ is said to be an equivalent relation on the set S.

Example:

The identity relation and the global relation on the (1) set are equivalent.

(2) congruence relation of triangles, and similarity relation of triangles is equivalent relation.

(3) The relationship of "the same age" in a class is equivalent.