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Need solution for RD Sharma maths Class 12 Chapter Relation Exercise 1.1 Question 6 maths textbook solution.

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R is neither reflexive nor symmetric nor transitive.


A relation R on set A is

 Reflexive relation:

If  (a,a)\in \; R for every a\in \; R

Symmetric relation:

If (a,b) is true then (b,a)  is also true for every a, b \in A

Transitive relation:

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

Given : R=\{(a, b): b=a+1\}

Solution :

Let a be an arbitrary element of set A.


     a=a+1 cannot be true for all a\; \in\; A

     (a, a) \notin R

     So, R is not reflexive on A

Symmetry :

\begin{aligned} &\text { Let }(a, b) \in R\\ &b=a+1\\ &a=b-1\\ &-a=-b+1\\ &\text { Thus }\\ &(b, a) \notin R \end{aligned}

So, R is not symmetric on A

Transitivity :

Let (1,2) \text { and }(2,3) \in R

\begin{aligned} &2=1+1 \text { and } \\ &3=2+1 \text { is true } \\ &\text { But } 3 \neq 1+1 \\ &(1,3) \notin R \end{aligned}

So, R is not transitive on A

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