Equivalence relations are binary relations that satisfy the following property:

For a relation (denoted as where and are arbitrary values in the domain) to be called equivalence relation, they need to satisfy the following property:

  • Reflexive:
  • Symmetric:
  • Transitive:

Strict equivalent is just one kind of equivalence. We can also have other kind of equivalence relationship that satisfy the above properties.

Example

For a set , we can have an equivalence relation .

References