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Please Solve R. D. Sharma class 12 Chapter relations Exercise 1.1 Question 8  Maths textbook Solution.

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Hence, prove every identity relation on a set is reflexive but the converse is not necessarily true.


A relation R on set A is

 Reflexive relation:

If (a, a) \in R for everya \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: Every Identity relation is reflexive.


Let A be a set A=\{1,2,3\}

Then,  I_{A}=\{(1,1),(2,2),(3,3)\}

Identity relation is reflexive, since (a, a) \in A \quad \forall a

The converse of it need not be necessarily true.

Counter example:

Consider the set A=\{1,2,3\}


    RelationR=\{(1,1),(2,2),(3,3),(2,1),(1,3)\} is reflexive on A

However, R is not an identity relation.

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