# NCERT Solutions of Class 12 Maths | CBSE Textbook Solutions | Chapter 1 | Relations and Functions | Exercise 1.1 | Question 5 |

Question Details
 Board CBSE Book NCERT Textbook Class 12 Subject Mathematics Chapter 1 [Relations and Functions] Exercise 1.1 Question No. 5 Question Type Exercise

Check whether the relation $$\mathrm{R}$$ in $$\mathbf{R}$$ defined by $$\mathrm{R}=\left\{(a, b): a \leq b^3\right\}$$ is reflexive, symmetric or transitive.

Solution: $$R=\left\{(a, b): a \leq b^3\right\}, A=(-\infty, \infty)$$ or $$R$$
(a) Reflexive : $$R=\left\{(a, a): a \leq a^3 \Rightarrow a\left(a^2-1\right) \geq 0\right.$$
This is not true of all $$a \in A$$. So not reflexive.
(b) Symmetric : $$R=\left\{\left(a_1, a_2\right): a_1 \leq a_2^3\right\}$$ $$R=\left\{\left(a_2, a_1\right): a_2 \leq a_1^3\right\}$$ so not symmetric.
(c) Transitive : $$R=\left\{\left(a_1, a_2\right): a_1 \leq a_2^3\right\}$$
$R=\left\{\left(a_2, a_3\right): a_2 \leq a_3^3\right\} \Rightarrow a_2^3 \leq a_3^9$
So, $$a_1 \leq a_3^9 \nRightarrow a_1 \leq a_3^3$$. Not transitive.

5/5

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