Q. 84.2( 5 Votes )

Write the following relations as sets of ordered pairs and find which of them are functions:

i. {(x, y): y = 3x, x {1, 2, 3}, y {3, 6, 9, 12}}

ii. {(x, y): y > x + 1, x = 1, 2 and y = 2, 4, 6}

iii. {(x, y): x + y = 3, x, y {0, 1, 2, 3}}

Answer :

i. {(x, y): y = 3x, x {1, 2, 3}, y {3, 6, 9, 12}}


When x = 1, we have y = 3(1) = 3


When x = 2, we have y = 3(2) = 6


When x = 3, we have y = 3(3) = 9


Thus, R = {(1, 3), (2, 6), (3, 9)}


Every element of set x has an ordered pair in the relation and no two ordered pairs have the same first component but different second components.


Hence, the given relation R is a function.


ii. {(x, y): y > x + 1, x = 1, 2 and y = 2, 4, 6}


When x = 1, we have y > 1 + 1 or y > 2 y = {4, 6}


When x = 2, we have y > 2 + 1 or y > 3 y = {4, 6}


Thus, R = {(1, 4), (1, 6), (2, 4), (2, 6)}


Every element of set x has an ordered pair in the relation. However, two ordered pairs (1, 4) and (1, 6) have the same first component but different second components.


Hence, the given relation R is not a function.


iii. {(x, y): x + y = 3, x, y {0, 1, 2, 3}}


When x = 0, we have 0 + y = 3 y = 3


When x = 1, we have 1 + y = 3 y = 2


When x = 2, we have 2 + y = 3 y = 1


When x = 3, we have 3 + y = 3 y = 0


Thus, R = {(0, 3), (1, 2), (2, 1), (3, 0)}


Every element of set x has an ordered pair in the relation and no two ordered pairs have the same first component but different second components.


Hence, the given relation R is a function.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Trigonometric Functions - 0568 mins
Trigonometric Functions - 0152 mins
Conditional Identities31 mins
Trigonometric Functions - 0658 mins
Questions Discussion of Biomolecules48 mins
Let's Play the Game of Inequalities52 mins
Trigonometric Functions - 0366 mins
Trigonometric Functions - 0865 mins
Trigonometric Functions - 0760 mins
Master Solving Problems of trigonometry45 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses