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Need Solution for R. D.Sharma Maths Class 12 Chapter relations  Exercise 1.1 Question 14 sub question 5 Maths Textbook Solution.

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Answer:  R=\{(a, b): a<b\}


A relation R on set A is

 Reflexive relation:

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


We have to give the example of a relation which is transitive but neither symmetric nor reflexive.


The relation having properties of being transitive but neither symmetric nor reflexive.

Consider a relation R in R defined as:

R=\{(a, b): a<b\}

For any a \in R we have (a, a) \notin R, since a can’t be strictly less than a itself.

 Infact a=a

∴   Relation R is not reflexive.

Now, (1,2) \in R(\text { as } 1<2)

But 2 is not less than 1

∴   (2,1) \notin R

∴   R  is not symmetric

Now let (a, b),(b, c) \in R

\begin{aligned} &a<b \text { and } b<c \\ &a<c \\ &(a, c) \in R \end{aligned}

R is transitive.

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