CBSE Class 12 Mathematics Chapter-01 Relation and Function TYPES OF RELATIONS: Empty Relation : It is the relation R in X given by R =  ϕ ⊂ ϕ ⊂   X × X X × X . Universal Relation : It is the relation R in X given by R =  X × X X × X . Reflexive Relation : A relation R in a set A is called reflexive if (a, a) ∈ R for every a ∈ A. Symmetric Relation : A relation R in a set A is called symmetric if ( ,  ) ∈ R implies that ( ,  ) ∈ R, for all  ,   ∈ Transitive Relation : A relation R in a set A is called transitive if ( ,  ) ∈ R, and ( ,  ) ∈ R together imply that all  ,  ,   ∈ A. EQUIVALENCE RELATION :  A relation R in a set A is said to be an equivalence relation if R is reflexive, symmetric and transitive. Equivalence Classes:  Every arbitrary equivalence relation R in a set X divides X into mutually disjoint subsets (Ai) called partitions or subdivisions of X satisfying the following conditions: All elements of Ai are related to each other for all i. No element of Ai is related to an