# NCERT Solutions of Class 12 Maths | CBSE Textbook Solutions | Chapter 1 | Relations and Functions | Exercise 1.1 | Question 3 |

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 Board CBSE Book NCERT Textbook Class 12 Subject Mathematics Chapter 1 [Relations and Functions] Exercise 1.1 Question No. 3 Question Type Exercise

Check whether the relation $$R$$ defined in the set $$\{1,2,3,4,5,6\}$$ as $$\mathbf{R}=\{(a, b): b=a+1\}$$ is reflexive, symmetric or transitive.

$$\mathrm{R}=\{(\mathrm{a}, \mathrm{b}): \mathrm{b}=\mathrm{a}+1\}$$ in the set $$\{1,2,3,4,5,6\}$$.
$$\therefore \mathrm{R}=\{(1,2),(2,3),(3,4),(4,5),(5,6)\}$$.
(i) $$\because(1,1) \notin \mathrm{R} \Rightarrow \mathrm{R}$$ is not reflexive.
(ii) $$\because(1,2) \in \mathrm{R}$$ but $$(2,1) \notin \mathrm{R} . \Rightarrow \mathrm{R}$$ is not symmetric.
(iii) $$\because(1,2),(2,3) \in \mathrm{R}$$, but $$(1,3) \notin \mathrm{R} . \Rightarrow \mathrm{R}$$ is not transitive.

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