# NCERT Solutions of Class 12 Maths | CBSE Textbook Solutions | Chapter 1 | Relations and Functions | Exercise 1.1 | Question 2 |

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 Board CBSE Book NCERT Textbook Class 12 Subject Mathematics Chapter 1 [Relations and Functions] Exercise 1.1 Question No. 2 Question Type Exercise

Question-2. Show that the relation $$\mathbf{R}$$ in the set $$\mathbf{R}$$ of real numbers, defined as $$\mathrm{R}=\left\{(a, b): a \leq b^2\right\}$$ is neither reflexive nor symmetric nor transitive.

(i) $$\mathrm{R}$$ is not reflexive, $$\because$$ a is not less than or equal to $$\mathrm{a}^2$$ for all $$\mathrm{a} \in \mathrm{R}$$, e.g., $$\frac{1}{2}$$ is not less than $$\frac{1}{4}$$.
(ii) $$\mathrm{R}$$ is not symmetric since if $$\mathrm{a} \leq \mathrm{b}^2$$ then $$\mathrm{b}$$ is not less than or equal to $$\mathrm{a}^2$$, e.g. $$2<5^2$$ but 5 is not less than $$2^2$$.
(iii) $$\mathrm{R}$$ is not transitive : If $$\mathrm{a} \leq \mathrm{b}^2, \mathrm{~b} \leq \mathrm{c}^2$$, then a is not less than $$\mathrm{c}^2$$, e.g. $$2<(-2)^2,-2<(-1)^2$$, but 2 is not less than $$(-1)^2$$.

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