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


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Ex 1.1, 15 Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Choose the correct answer. (A) R is reflexive and symmetric but not transitive. (B) R is reflexive and transitive but not symmetric. (C) R is symmetric and transitive but not reflexive. (D) R is an equivalence relation. R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Check Reflexive If the relation is reflexive, then (a, a) ∈ R for every a ∈ {1, 2, 3, 4} Since (1, 1), (2, 2), (3, 3) & (4, 4) ∈ R. ∴ R is reflexive Check symmetric To check whether symmetric or not, If (a, b) ∈ R, then (b, a) ∈ R Here (1, 2) ∈ R , but (2, 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 Here, (1, 3) ∈ R and (3, 2) ∈ R & (1, 2) ∈ R. ∴ R is transitive Hence, R is reflexive and transitive but not symmetric. The correct answer is B.

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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.