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

Answers (1)

Answer:

$R$ is neither reflexive nor symmetric nor transitive.

Hint:

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.

Then,

$a=a+1$ 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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