is the codomain of this relation. A Note The total number of relations that can be defined from a set A to a set B is the number of possible subsets of A × B. If n (A ) = p and n (B) = q , then n (A × B) = pq and the total number of relations is pq . Example Let A = { , } and B = { , }.
Find the number of relations from A to B. Solution We have, A × B = {( , ), ( , ), ( , ), ( , )}. Since n (A × B ) = , the number of subsets of A × B is . Therefore, the number of relations from A into B will be .
Remark A relation R from A to A is also stated as a relation on A. EXERCISE . . Let A = { , , ,..., }.
Define a relation R from A to A by R = {( x , y ) : x – y = , where x , y ∈ A}. Write down its domain, codomain and range. Fig . Fig .
MATHEMATICS . Define a relation R on the set N of natural numbers by R = {( x , y ) : y = x + , x is a natural number less than ; x , y ∈ N }. Depict this relationship using roster form. Write down the domain and the range.
. A = { , , , } and B = { , , }. Define a relation R from A to B by R = {( x , y ): the difference between x and y is odd; x ∈ A, y ∈ B}. Write R in roster form.
. The Fig2. shows a relationship between the sets P and Q. Write this relation (i) in set-builder form (ii) roster form.
What is its domain and range? . Let A = { , , , , }. Let R be the relation on A defined by {( a