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

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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


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


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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