Universal Relation
A relation R in a set A is called universal relation, if each element of A is related to every element of A
R = A × A.
Eg: Girls school R = {( a, b): Difference between age of a and b is less than 100 years }
Trivial Relations
Both the empty relation and the universal relation are sometimes called trivial relations.
Reflexive Relations A relation R in a set A is called reflexive, if( a, a) ∈ R, for every a∈ A Let’ s take set A =( 1,4,5 }
If Relation R ={( 1,1),( 4,4),( 5,5), ……….}, then relation R is called Reflexive relation.
Symmetric Relations
A relation R in set A is called symmetric, if( a1, a2) ∈ R implies( a2, a1) ∈ R, for all a1, a2 ∈ A.
Let’ s take set A =( 1,4,5 }
If Relation R ={( 1,4),( 4,1),( 1,5),( 5,1),( 4,5),( 5,4) ……….}, then relation R is called Reflexive relation.
E. g.: Height of Boys R = {( a1, a2): Height of a1 is equal to height of a2 } Height of a1 is equal to height of a2 à Height of a2 is equal to height of a1 Example of Non-symmetric relation Height of Boys R = {( a1, a2): Height of a1 is greater than height of a2 }
Height of a1 is greater than height of a2 XàX Height of a2 is greater than height of a1
Transitive relations
A relation R in a set A is called transitive, if( a1, a2) ∈ R and( a2, a3) ∈ R implies that( a1, a3) ∈ R, for all a1, a2, a3 ∈ A. E. g.: Height of Boys R = {( a1, a2, a3): Height of a1 is equal to height of a2 & Height of a2 is equal to height of a3 à Height of a1 is equal to height of a3 }