# NCERT Solutions of Class 12 Maths | CBSE Textbook Solutions | Chapter 1 | Relations and Functions | Exercise 1.1 | Question 7 |

Question Details
 Board CBSE Book NCERT Textbook Class 12 Subject Mathematics Chapter 1 [Relations and Functions] Exercise 1.1 Question No. 7 Question Type Exercise

Show that the relation R in the set A of all the books in a library of a college, given by $$\mathrm{R}=\{(x, y): x$$ and $$y$$ have same number of pages $$\}$$ is an equivalence relation.

Solution:

$$A=$$ all books in library.
$$R=\{(x, y): x$$ and $$y$$ have same number of pages $$\}$$
(a) Reflexive : $$R=\{(a, a): a$$ and $$a$$ have same number of pages $$\}$$. True so reflexive.
(b) Symmetric: If $$R=\left\{\left(a_1, a_2\right): a_1\right.$$ and $$a_2$$ have same no. of pages $$\}$$
Thus, $$R=\left\{\left(a_2, a_1\right): a_2\right.$$ and $$a_1$$ will definitely have same no. of pages $$\}$$. So, symmetric.
(c) Transitive : If $$R=\left\{\left(a_1, a_2\right)\right\}$$ and $$R=\left\{\left(a_2, a_3\right)\right\}$$
So, $$a_1, a_2$$ and $$a_3$$ all three books will have same no. of pages. Thus, $$R=\left\{\left(a_1, a_3\right)\right\}$$ is true. So reflexive. Therefore, equivalence relation.

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