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


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Ex 1.1, 10 Given an example of a relation. Which is (iii) Reflexive and symmetric but not transitive. Let A = {1, 2, 3}. Let relation R on set A be Let R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (1, 3), (3, 1)} 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 reflexive Check Symmetric To check whether symmetric or not, If (a, b) ∈ R, then (b, a) ∈ R Since, If (1, 2) ∈ R , then (2, 1) ∈ R & if (1, 3) ∈ R , then (3, 1) ∈ R ∴ R is symmetric. Check transitive To check whether transitive or not, If (a,b) ∈ R & (b,c) ∈ R , then (a,c) ∈ R Here, a = 1, b = 2 or 3, but there is no c (no third element) Hence ,R is not transitive Hence, relation R is reflexive and symmetric but not 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.