This page contains the NCERT mathematics class 12 chapter Relations and Functions Exercise 1.1 Problem 6 Solution. Solutions for other problems are available at Exercise 1.1 Solutions
Exercise 1.1 Problem 6 Solution
6. Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.
To Check whether R is Reflexive: The relation R in the set A is reflexive if (a, a) ∈ R, for every a ∈ A.
We have, 1 ∈ A but (1, 1) ∉ R
∴ R is not 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
We see that both (1, 2) ∈ R and (2, 1) ∈ 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
We see that (1, 2) ∈ R, (2, 1) ∈ R. But (1, 1) ∉ R
∴ R is not Transitive
∴ R is symmetric but neither reflexive nor transitive.
