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).
definition
Let R be a binary relation on set A, if R satisfies:
Reflexivity:? a∈A，= & gt(a，a)∈R .
Symmetry: (a, b) ∈ r ∧ a ≠ b = > (b，a)∈R .
Transitivity: (a, b)∈R, (b, c) ∈ r = > (a，c)∈R .
Then r is said to be an equivalent relationship defined on a.