Ex 1.1, 10 (iii) - Chapter 1 Class 12 Relation and Functions

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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.