This page contains the NCERT mathematics class 12 chapter Relations and Functions Exercise 1.1 Problem 7 Solution. Solutions for other problems are available at Exercise 1.1 Solutions
Exercise 1.1 Problem 7 Solution
7. 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.
To Check whether R is Reflexive: The relation R in the set A is reflexive if (a, a) ∈ R, for every a ∈ A.
If we consider a book x, it will have the same number of pages as itself. i.e. x.
⇒ (x, x) ∈ R
∴ R is Reflexive
To Check whether R is Symmetric: The relation R in the set A is symmetric if (a_1, a_2) ∈ R implies that (a_2, a_1) ∈ R, for all a_1, a_2 ∈ A
If book x has the same number of pages as book y, then book y will also have the same number of pages as book x.
⇒ If (x, y) ∈ R then (y, x) ∈ R
∴ R is symmetric
To Check whether R is Transitive: The relation R in the set A is transitive if (a_1, a_2) ∈ R and (a_2, a_3) ∈ R implies that (a_1, a_3) ∈ R, for all a_1, a_2, a_3 ∈ A
If book x has the same number of pages as book y and book y has the same number of pages as book z, then it implies that book x has the same number of pages as book z.
⇒ if (x, y) ∈ R and (y, z) ∈ R then (x, z) ∈ R
∴ R is Transitive
∴ R is reflexive, symmetric and transitive, it is an equivalence relation.
