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


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Ex 1.1, 1 Determine whether each of the following relations are reflexive, symmetric and transitive: (ii) Relation R in the set N of natural numbers defined as R = {(x, y): y = x + 5 and x < 4} R = {(x, y): y = x + 5 and x < 4} Here x & y are natural numbers, & x < 4 So, we take value of x as 1 , 2, 3 ∴ R = {(1, 6), (2, 7), (3, 8)} Check Reflexive If the relation is reflexive, then (a, a) ∈ R for every a ∈ N Since (1, 1) ∉ R ∴ R is not reflexive Check symmetric To check whether symmetric or not, If (a, b) ∈ R, then (b, a) ∈ R Here (1, 6) ∈ R , but (6, 1) ∉ R ∴ R is not symmetric Check transitive To check whether transitive or not, If (a, b) ∈ R & (b, c) ∈ R , then (a, c) ∈ R There is no pair in R such that (a, b) ∈ R and (b, c) ∈ R , then (a, c) ∉ R. ∴ R is not transitive Hence, R is neither reflexive, nor symmetric, nor transitive.

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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.