Definition of Relation

RELATION

Technical Definition

                                                                             

Let A and B be any sets defined as A = {a,b,c} and  B = {x,y,z} in the above figure then A*B = {(a,x),(b,x),(c,x),(a,y),(b,y),(c,y),(a,z),(b,y),(c,z))} is known as cartisian product then Relation  defined from  set A to B as a subset of A*B.

It is denoted as R,R={(a,y),(b,z),(c,z)} from the above picture

R is subset of A*B

Notation- either we can say (a,y) belongs to R or aRy (a R related to y) both are same                                                     

                                            Or

It is defined between two sets as a collection of ordered pairs containing one object from each set. ... A function is a type of relation. But, a relation is not a function because it is allowed to have the object in the first set to be related to more than one object in the second set.

                                             Or

It is a relationship between sets of values. In math, Relation is between the x-values and y-values of ordered pairs.  the set of all  x-values is known as domain, and the set of all y-values is known as range.