Relations

 Relation

The set of ordered pairs under certain conditions is called Relation. For example, 

Nischal is a student of class 8.
Kathmandu is the capital city of Nepal.
7 is the half of 14.

Hence, a relation from A to B can be defined as R: A → B OR R={(x,y): x∈A & y ∈ B}

Let's consider a relation R:M→N is defined as "is square of" where M = {1,4,9} and N = {1,3,5} then ,

R = {(1,1), (9,3)}   [As we know 4 is square of 2 but 2∉ N and 25 is square of  5 but 25 ∉ M.] 

Domain Co-domain and Range of a Relation.    

 

Types of relations:

Let R:M→N is a relation from M to N then the following relations are possible. 

1) One to one relation 

2) Many to one relation 

3)One to many Relation

Relations can be represented in various ways as follow: 

a) Set of ordered pair. 

b) Table 

c) Arrow diagram/Mapping diagram 

d) Graph 

e) Descripitive method.

Inverse Relation

A relation that can be obtained from interchanging x and y components of each ordered pairs of the given relation R is called Inverse Relation.