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

Question Details
BookNCERT Textbook
Chapter1 [Relations and Functions]
Question No.7
Question TypeExercise

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


\(A=\) 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.

Verified Answer

Share This Answer With Your School Friends


  • Our Answers are always accurate, since they are validated by prominent faculty members of Abstract Classes.
  • Although, if there is a problem with the above answer, please let us know and we will verify and rectify ourselves if we find a mistake.
  • In the future, we hope to establish a learning environment where every student is able to find the right answer.

Noticed a Mistake

Don't worry about it. You only need to copy the Question URL and then click the submit button below.

Search us like this in Google 🔍

CBSE Class 12 Maths Solution Abstract Classes NCERT Mathematics Solution Abstract Classes IGNOU Maths Assignment Solution IGNOU PGDAST Abstract Classes IGNOU Physics Abstract Classes

Bookmark This Awesome Website 

Leave a Comment

Scroll to Top
Scroll to Top