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

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Answer:   R=\{(5,6),(6,5)\}


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


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


\\\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.}


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