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Example 4 - Show R = {(1, 1), (2, 2),(3, 3), (1,2), (2,3)} - To prove relation reflexive/trasitive/symmetric/equivalent

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  1. Chapter 1 Class 12 Relation and Functions
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Example 4, Show that the relation R in the set {1, 2, 3} given by R = {(1, 1), (2, 2),(3, 3), (1, 2), (2, 3)} is reflexive but neither symmetric nor transitive. R = {(1, 1), (2, 2),(3, 3), (1, 2), (2, 3)} Check Reflexive If the relation is reflexive, then (a, a) ∈ R for every a ∈ {1,2,3} Since (1, 1) ∈ R ,(2, 2) ∈ R & (3, 3) ∈ 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, 2) ∈ R and (2, 3) ∈ R but (1,3) ∉ R. ∴ R is not transitive Hence, R is reflexive but neither symmetric nor transitive.

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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