# NCERT Solutions of Class 12 Maths | CBSE Textbook Solutions | Chapter 1 | Relations and Functions | Exercise 1.1 | Question 4 |

Question Details
 Board CBSE Book NCERT Textbook Class 12 Subject Mathematics Chapter 1 [Relations and Functions] Exercise 1.1 Question No. 4 Question Type Exercise

Show that the relation $$R$$ in $$R$$ defined as $$R=\{(a, b): a \leq b\}$$, is reflexive and transitive but not symmetric.

$$A=(-\infty, \infty)$$ or $$R$$
$$R=\{(a, b): a \leq b\}$$
(a) Reflexive : $$R=\{(a, a): a \leq a\}$$ so reflexive.
(b) Symmetric : $$R=\left\{\left(a_1, a_2\right): a_1 \leq a_2\right\}$$
$$R=\left(a_2, a_1\right): a_2 \leq a_1$$ so not symmetric.
(c) Transitive : $$R=\left\{\left(a_1, a_2\right): a_1 \leq a_2\right\}$$ and
$$R=\left\{\left(a_2, a_3\right): a_2 \leq a_3\right\}$$
Thus, $$a_1 \leq a_2 \leq a_3$$
$$\Rightarrow a_1 \leq a_3$$ so transitive.

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