Ex 1.1, 6 - In set {1, 2, 3}, R = {(1, 2), (2, 1)} is symmetric - Ex 1.1

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  1. Chapter 1 Class 12 Relation and Functions
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Ex 1.1, 6 Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive R = {(1, 2), (2, 1)} Check Reflexive If the relation is reflexive, then (a, a) ∈ R for every a ∈ {1,2,3} 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, 2) ∈ R , & (2, 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, (1, 2) ∈ R and (2, 1) ∈ R but (1, 1) ∉ R. ∴ R is not transitive Hence, R is symmetric but neither reflexive nor transitive.

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