| 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.
Expert Answer
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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