Definition: Equivalence Relation

• Let S be a set and r a relation between S and itself. We call r an equivalence relation on S if r has the following three properties:
  1. Reflexivity: Every element of S is related to itself
  2. Symmetry: If s is related to t then t is related to s
  3. Transitivity: If s is related to t and t is related to u, then s is related to u.