Check whether the following relations are reflexive, symmetric, transitive and anti-symmetric and hence verify that is the relation an equivalence relation. 1) The relation R={(1,2),(2,1),(3,2),(2,3)} on set A={1,2,3}. 2)The relation R={(1,2),(2,3),(1,3)} on set A={1,2,3}. 3)The relation R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2),(1,3),(3,1)} on set A={1,2,3}.

Check whether the following relations are reflexive, symmetric, transitive and anti-symmetric and hence verify that is the relation an equivalence relation. 1) The relation R={(1,2),(2,1),(3,2),(2,3)} on set A={1,2,3}. 2)The relation R={(1,2),(2,3),(1,3)} on set A={1,2,3}. 3)The relation R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2),(1,3),(3,1)} on set A={1,2,3}.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 28E

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