Check sibling questions

Ex 1.1, 10 - Given an example of a relation. Which is - Chapter 1 - To prove relation reflexive/trasitive/symmetric/equivalent

  Ex 1.1, 10 - Part 2

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Ex 1.1, 10 Given an example of a relation. Which is (i) Symmetric but neither reflexive nor transitive. Let A = {1, 2, 3}. Let relation R on set A be Let 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), (2, 2), (3, 3) R R is not reflexive Check Symmetric Since (1, 2) R , (2, 1) R So, If (a, b) R, then (b, a) R R is symmetric. Check transitive To check whether transitive or not, If (a, b) R & (b, c) R , then (a, c) R If a = 1, b = 2, but there is no c (no third element) Similarly, if a = 2, b = 1, but there is no c (no third element) Hence ,R is not transitive Hence, relation R is symmetric but not reflexive and transitive

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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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.