Ex 1.1, 10 Given an example of a relation. Which is (ii) Transitive but neither reflexive nor symmetric. Let R = {(a, b): a < b} Check reflexive Since a cannot be less than a a ≮ a So, (a, a) ∉ R ∴ R is not reflexive. Check symmetric If a < b , then b cannot be less than a i.e. b ≮ a So, if (a, b) ∈ R , (b, a) ∉ R ∴ R is not symmetric Check transitive If a < b & b < c, then a < c So, if (a, b) ∈ R, (b, c) ∈ R, then (a, c) ∈ R ∴ R is transitive. Hence, relation R is transitive but not reflexive and symmetric.

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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.