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.