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  • Need solution for RD Sharma maths Class 12 Chapter Relation Exercise 1.1 Question 5 Subquestion (iii) maths textbook solution.

Need solution for RD Sharma maths Class 12 Chapter Relation Exercise 1.1 Question 5 Subquestion (iii) maths textbook solution.

Answers (1)

Answer: Transitive neither reflexive nor symmetric.

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 :  a R b \text { if }|a| \leq b

Solution :

Reflexivity:

  Let -a be an arbitrary element of R

  Then -a \in R                                 

\Rightarrow|-a| \neq-a

So, R is not reflexive

Symmetry:

Let  (a, b) \in R

 \begin{aligned} &|a| \leq b \\ &|b| \lessgtr a \text { for all } a, b \in R \\ &(b, a) \notin R \end{aligned}

So, R is not symmetric.

Transitivity:

\begin{aligned} &\text { Let }(a, b) \in R_{\text {and }}(b, c) \in R \\ &|a| \leq b \text { and }|b| \leq c \text { for } a, b, c \in R \end{aligned}

Multiplying the corresponding sides, we get

\begin{aligned} &|a| \times|b| \leq b c \\ &|a| \leq c \\ &(a, c) \in R \end{aligned}

Thus, R is transitive

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