Question

Which of the following relations are functions? Give reason.

(i). R = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5)} 

(ii). R = {(2, 1), (2, 2), (2, 3), (2, 4)} 

(iii). R = {(1, 2), (2, 5), (3, 8), 4, 10), 5, 12), (6, 12)}

Answer 1

A function is a relation in which each element of the domain is paired with exactly one element of the range. 

(i). Given, 

R = {(1,1), (2, 2), (3, 3), (4, 4), (4, 5)} 

The above relations is not a function because 4 has two images. 

(ii). Given, 

R = {(2, 1), (2, 2), (2, 3), (2, 4)} 

The above relation is not a function because does not have a unique image. 

(iii). Given, 

{(1, 2), (2, 5), (3, 8), (4, 10), (5, 12), (6, 12)} 

The above relation is a function because every elements in the domain has its unique image.