Each equivalence relation on a set corresponds to a partition of the set, and each partition of the set corresponds to an equivalence relation of the set. Different equivalence relations correspond to different divisions of sets, so there are many different equivalence relations. The ternary set * * * has five different divisions (there are 1 block and 1 block, and there are three blocks).

If A={ 1, 2,3}, these five different types are divided into

{{ 1}, {2}, {3}}; {{ 1}, {2,3}}; {{ 1,3}, {2}}; {{ 1,2}, {3}}; {{ 1, 2, 3}};

The corresponding equivalent relationship is

R 1={( 1， 1)，(2，2)，(3，3)}； R2={( 1， 1)，(2，2)，(2，3)，(3，2)，(3，3)}；

R3={( 1， 1)，( 1，3)，(3， 1)，(2，2)，(3，3)}；

R4={( 1， 1)，( 1，2)，(2 1)，(2，2)，(3，3)}；

R5={( 1， 1)、(2，2)、(3，3)、( 1，2)、(2，3)、(3，2)、( 1，3)、(3， 1)}；

Generally speaking, the set of n elements has Bn different divisions (equivalence relations).

Bn=2n！ /((n+ 1)n！ n！ ), such as a group of four elements, can determine 14 equivalence relations.