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14.1

Please Solve R.D. Sharma class 12 Chapter relations Exercise 1.1 Question 14 sub question 1 Maths textbook Solution.

Answers (1)

Answer:

$R=\{(4,4),(6,6),(8,8),(4,6),(6,4),(6,8),(8,6)\}$

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:

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

Solution:

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

Let a relation $R$ on $A$ as $R=\{(4,4),(6,6),(8,8),(4,6),(6,4),(6,8),(8,6)\}$

Relation $R$ is reflexive since for every $a \in A,(a, a) \in R \text { i.e }(4,4),(6,6),(8,8) \in R$

Relation $R$ is not transitive since $(4,6),(6,8) \in R \text { but }(4,8) \notin R$

Relation $R$ is symmetric since $(a, b) \in R \Rightarrow(b, a) \in R \text { for all } b \in R$

Hence, relation $R$ is reflexive and symmetric but not transitive.

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