equivalence relations

Complete

Summary

Equivalance relation

  • a relation that is reflexive, symmetric and transitive

Partitions

  • set of nonempty, pairwise disjoint subsets

pairwise disjont -> for every subset, compared to every other subset, they do not intersect

Equivalence classes

  • a subset of the equivalence relation

Concept

Partition induced by an equivalence relation (Theorem 2.6)

Application

Partitions/eqquivalence classes of

  • undirected graph since its symmetric
  • each node has a loop since its reflexive
  • all nodes are interconnected within its subset since its transitive
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is a congruence modulo 4 relation