Numerical : Let A = { 1 , 2 , 3 , 4 , 5 , 6 }. Define a relation R from A to A by R = {( x , y ) : y = x + 2 }. Depict this relation using an arrow diagram & set builder form . Write down the domain , codomain and range of R .
Solution : Lets fist create arrow diagram
Relation A X A = ( 1,3 ) ,( 2,4 ) , ( 3 , 5 ) , ( 4,6 )
Number of Relations It is number of possible subsets of A × B .
If n ( A ) = p and n ( B ) = q , then n ( A × B ) = pq , Thus total number of relations / subset is 2 pq . Example : Let ’ s find number of relation for A = { 1 , 2 } and B = { 3,4,5 }.
Here p = 2 & q = 3 , so pq = 2 * 3 = 6
2 6 = 64 , thus it can have 64 relations . Note that relation R from A to A is also stated as a relation on A .
Functions : In terms of Relation
A relation is said to be a function if every element of set A has only 1 image / output in set B . Note that other way round need not be true , more than 1 elements of Set A can have same image / output in set B . E . g . two elements of Set A 5 & -5 correspond to element 25 of Set B , still it is a function .