A relation R in 𝑆 = {1,2,3} is defined as 𝑅 = {(1, 1), (1, 2), (2, 2), (3, 3)}. Which element(s) of relation R be removed to make R an equivalence relation?

A relation R in S = {1,2,3} is defined as R = {(1, 1), (1, 2), (2, 2)

 

  1. Class 12
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Transcript

Question 2 A relation R in 𝑆 = {1, 2, 3} is defined as 𝑅 = {(1, 1), (1, 2), (2, 2), (3, 3)}. Which element(s) of relation R be removed to make R an equivalence relation? R = {(1, 1), (1, 2), (2, 2), (3, 3)} Here, since we have (1, 2), We need to have (2, 1) also… to make it symmetric But, if we remove (1, 2), Then our Relation can be symmetric, reflexive and transitive i.e. equivalent Thus, we remove (1, 2)

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.