Relations and Functions

đŸĢ CBSEClass 12Mathematics

💡 Equivalence Relation

A relation R on a set A is an Equivalence Relation if it satisfies three properties:

  1. Reflexive: (a, a) ∈ R for every a ∈ A.
  2. Symmetric: If (a, b) ∈ R, then (b, a) ∈ R.
  3. Transitive: If (a, b) ∈ R and (b, c) ∈ R, then (a, c) ∈ R. An equivalence relation divides a set into disjoint equivalence classes.

💡 Types of Relations

A relation can be: * Reflexive * Symmetric * Transitive