Question

Let A = {1, 2, 3, 4, 5, 6}. Define a relation on set A by R = {(X, Y): y = x +1}

(i) Depict this relation using an arrow diagram.

(ii) Write down the domain, codomain and range of R.

Answer 1

Given, A = {1, 2, 3, 4, 5, 6} and define a relation on set A is R = $(X,Y):y=x+1$

On putting x = 1, 2, 3, 4, 5, 6 in y = x + 1, we get

y = 2, 3, 4, 5, 6, 7

For x = 6, we get

y = 7 which does not belong to set A.

$\therefore$ R = {(1,2),(2,3),(3,4),(4,5),(5,6)}

(i) The corresponding arrow diagram representing R is as follows :

(ii) It is clear from the arrow diagram, domain = {1,2,3,4,5} codomain = {1,2,3,4,5,6} and range = {2,3,4,5,6}