Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Ex 1.1, 4 Show that the relation R in R defined as R = {(a, b) : a ≤ b}, is reflexive and transitive but not symmetric. R = { (a, b) : a ≤ b } Here R is set of real numbers Hence, both a and b are real numbers Check reflexive We know that a = a ∴ a ≤ a ⇒ (a, a) ∈ R ∴ R is reflexive. Check symmetric To check whether symmetric or not, If (a, b) ∈ R, then (b, a) ∈ R i.e., if a ≤ b, then b ≤ a Since b ≤ a is not true for all values of a & b Hence, the given relation is not symmetric Check transitive If a ≤ b, & b ≤ c , then a ≤ c ∴ If (a, b) ∈ R & (b, c) ∈ R , then (a, c) ∈ R Hence, the given relation is transitive Hence, R = {(a, b) : a ≤ b}, is reflexive and transitive but not 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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.