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.

Solution:

A = {1, 2, 3}

R = {(1, 2), (2, 1)}

(1, 1), (2, 2), (3, 3) ∉ R [ ∉ represents does not belong to ]

Therefore,

R is not reflexive.

(1, 2) ∈ R and (2, 1) ∈ R

Therefore,

R is symmetric.

(1, 2) ∈ R and (2, 1) ∈ R

(1, 1) ∈ R

Therefore,

R is not transitive.

R is symmetric but neither reflexive nor transitive

---

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

Summary:

The relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive