Which of the following relations are functions? Give reason.(i). R = {

1.	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» 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.

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»

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.