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

Class 12, NCERT Chapter 1,  Exercise 1.1, Q7


Set A is the set of all books in the library of a college.



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



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



Let (x, y) ∈ R 



⇒ x and y have the same number of pages.



⇒ y and x have the same number of pages.



⇒ (y, x) ∈ R



∴R is symmetric.



Now, let (x, y) ∈R and (y, z) ∈ R.



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



⇒ x and z have the same number of pages.



⇒ (x, z) ∈ R



∴R is transitive.



Hence, R is an equivalence relation.
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