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Provide Solution For  R.D. Sharma Maths Class 12 Chapter relations  Exercise 1.1 Question 14  sub question 3 Maths Textbook Solution.

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Answer: R=\{(-5,-6),(-6,-5),(-5,-5)\}

Hint:

 A relation R on set A is

 Reflexive relation:

If (a, a) \in Rfor every a \in A

Symmetric relation:

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

Transitive relation:

\text { If }(a, b) \text { and }(b, c) \in R \text { , then }(a, c) \in R \text { for every } \mathrm{a}, \mathrm{b}, \mathrm{c} \in A

Given:

We have to give the example of a relation which is symmetric and transitive but not reflexive.

Solution:

The relation having properties of being symmetric and transitive but not reflexive.

Let A=\{-5,-6\}

Define a relation R on A as

R=\{(-5,-6),(-6,-5),(-5,-5)\}

Relation R is not reflexive as (-6,-6) \notin R

Relation R is symmetric as (-5,-6),(-6,-5) \in R

It is seen that (-5,-6),(-6,-5) \in R

Also (-5,-5) \in R

The relation R is transitive.

Hence relation R is symmetric and transitive but not reflexive.

 

 

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