Ex 1.1

Chapter 1 Class 12 Relation and Functions
Serial order wise

### Transcript

Ex 1.1, 10 Given an example of a relation. Which is (v) Symmetric and transitive but not reflexive. Let A = {1, 2, 3}. Let relation R on set A be Let R = {(1, 2), (2, 1), (1, 3), (3, 1), (2, 3), (3, 2)} Check Reflexive If the relation is reflexive, then (a, a) ∈ R for every a ∈ {1,2,3} Since (1, 1), (2, 2), (3, 3) ∉ R ∴ R is not reflexive Check Symmetric Since (1, 2) ∈ R , (2, 1) ∈ R & (1, 3) ∈ R , (3, 1) ∈ R & (2, 3) ∈ R , (3, 2) ∈ R So, If (a, b) ∈ R, then (b, a) ∈ R ∴ R is symmetric. Check transitive Since (1, 2) ∈ R , (2, 3) ∈ R & (1, 3) ∈ R & (2, 1) ∈ R , (1, 3) ∈ R & (2, 3) ∈ R & (3, 1) ∈ R , (1, 2) ∈ R & (3, 2) ∈ R So, If (a, b) ∈ R , (b, c) ∈ R , then (a, c) ∈ R ∴ R is transitive. Hence, relation R is symmetric and transitive but not reflexive

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.