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

Solution:

R = {(x, y) : x and y have same number of pages}

R is reflexive since (x, x) ∈ R as x and x have the same number of pages.

Therefore,

R is reflexive.

(x, y) ∈ R

x and y have the same number of pages and y and x have the same number of pages (y, x) ∈ R

Therefore,

R is symmetric.

(x, y) ∈ R, (y, z) ∈ R

x and y have the same number of pages, y and z have the same number of pages.

Then x and z have the same number of pages.

( x, z ) ∈ R

Therefore,

R is transitive.

R is an equivalence relation

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NCERT Solutions for Class 12 Maths - Chapter 1 Exercise 1.1 Question 7

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

Summary:

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