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

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.

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