Get Answers to all your Questions

header-bg qa

Explain solution for RD Sharma Class 12 Chapter Relation Exercise 1.1 Question 15 Maths textbook solution.

Answers (1)

Answer : R=\{(1,2),(2,3),(1,1),(2,2),(3,3),(3,2),(2,1),(1,3),(3,1)\}

Hint :

A relation R on set A is

 Reflexive relation: a, b, c \in A

If  (a, a) \in R for every a \in A

Symmetric relation:

If (a,b) is true then (b,a)  is also true for every a, b \in A

Transitive relation:

If  (a,b) and , then (b, c) \in R  for every (a, c) \in R

Given :

\begin{aligned} &\text { Relation } R=\{(1,2),(2,3)\} \text { on the set }\\ &A=\{1,2,3\} \end{aligned}

Solution :

To make R reflexive we will add (1,1),(2,2),(3,3) to get R^{\prime}=\{(1,2),(2,3),(1,1),(2,2),(3,3)\}  is reflexive.

Again, to make R symmetric we will add (3,2) and (2,1)  R^{\prime \prime}=\{(1,2),(2,3),(1,1),(2,2),(3,3),(3,2),(2,1)\}is reflexive and symmetric .

To make R transitive we will add (1,3) and (3,1) R^{\prime \prime \prime}=\{(1,2),(2,3),(1,1),(2,2),(3,3),(3,2),(2,1),(1,3),(3,1)\} is reflexive and symmetric and transitive.

Posted by


View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support