#### Explain Solution R. D. Sharma Class 12 Chapter relations Exercise 1.1 Question 14 sub question 4 maths Textbook Solution.

Answer:   $R=\{(5,6),(6,5)\}$

Hint:

A relation R on set A is

Reflexive relation:

If $(a, a) \in R$ for 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:

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

Given:

$\text { Let } A=\{5,6,7\} \text { . }$

Solution:

$\\\text{Define a relation R on A as R}=\{(5,6),(6,5)\}. \\\text{Relation R is not reflexive as }(5,5),(6,6),(7,7) \notin \mathrm{R}.$

\begin{aligned} &\text { Now, as }(5,6) \in \mathrm{R} \text { and also }(6,5) \in \mathrm{R}, \mathrm{R} \text { is symmetric. }\\ &\Rightarrow(5,6),(6,5) \in \mathrm{R}, \text { but }(5,5) \notin \mathrm{R} \end{aligned}

$\\\text{Therefore, R is not transitive. }\\ \text{Hence, relation R is symmetric but not reflexive or transitive.}$