# Find the inverse

An inverse relation is the set of ordered pairs obtained by interchanging the first and second elements of each pair in the original relation. If the graph of a function contains a point (a, b), then the graph of the inverse relation of this function contains the point (b, a).

i. Given, R= {(1, 2), (1, 3), (2, 3), (3, 2), (5, 6)}

R‑1 = {(2, 1), (3, 1), (3, 2), (2, 3), (6, 5)}

R‑1 = {(2, 1), (2, 3), (3, 1), (3, 2), (6, 5)}

ii. Given, R= {(x, y) : x, y N; x + 2y = 8}

Here, x + 2y = 8

x = 8 – 2y

As y N, Put the values of y = 1, 2, 3,…… till x N

On putting y=1, x = 8 – 2(1) = 8 – 2 = 6

On putting y=2, x = 8 – 2(2) = 8 – 4 = 4

On putting y=3, x = 8 – 2(3) = 8 – 6 = 2

On putting y=4, x = 8 – 2(4) = 8 – 8 = 0

Now, y cannot hold value 4 because x = 0 for y = 4 which is not a natural number.

R = {(2, 3), (4, 2), (6, 1)}

R‑1 = {(3, 2), (2, 4), (1, 6)}

R‑1 = {(1, 6), (2, 4), (3, 2)}

iii. Given, R is a relation from {11, 12, 13} to (8, 10, 12} defined by y = x – 3

Here,

x {11, 12, 13} and y (8, 10, 12}

y = x – 3

On putting x = 11, y = 11 – 3 = 8 (8, 10, 12}

On putting x = 12, y = 12 – 3 = 9 (8, 10, 12}

On putting x = 13, y = 13 – 3 = 10 (8, 10, 12}

R = {(11, 8), (13, 10)}

R‑1 = {(8, 11), (10, 13)}

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
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
RELATED QUESTIONS :

Find the inverse RD Sharma - Mathematics

A relation R is dRD Sharma - Mathematics

Write the followiRD Sharma - Mathematics

Determine the domRD Sharma - Mathematics

Let A = {3, 5} anRD Sharma - Mathematics

Let A = {1, 2} anRD Sharma - Mathematics

Write the followiRD Sharma - Mathematics

Write the followiRD Sharma - Mathematics

Let A= {1, 2, 3, RD Sharma - Mathematics