# NCERT Solutions of Class 12 Maths | CBSE Textbook Solutions | Chapter 1 | Relations and Functions | Exercise 1.1 | Question 6 |

Question Details
 Board CBSE Book NCERT Textbook Class 12 Subject Mathematics Chapter 1 [Relations and Functions] Exercise 1.1 Question No. 6 Question Type Exercise

Show that the relation $$R$$ in the set $$\{1,2,3\}$$ given by $$R=\{(1,2),(2,1)\}$$ is symmetric but neither reflexive nor transitive.

Solution:

$A=\{1,2,3,\}: R=\{(1,2),(2,1)\}$
(a) Reflexive : $$R=\{(a, a)\}$$ where $$a \in A$$. $$=\{(1,1),(2,2),(3,3)\}$$ this is not true so not reflexive.
(b) Symmetric : $$R=\left\{\left(a_1, a_2\right)\right\}$$ and $$R=\left\{\left(a_2, a_1\right)\right\}$$ as $$(1,2) \in R$$ as well as $$(2,1) \in R$$. So symmetric.
(c) Transitive : $$R=\left\{\left(a_1, a_2\right)\right\}$$ and $$R=\left\{\left(a_2, a_3\right)\right\}$$. Not transitive.

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