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 }