Check if the following relations on the set P = {1,2,3,4,5} are reflexive,symmetric, antisymmetric and transitive. Justify your answer.(a) R1 = {(1,1),(1,2),(1,3),(1,5),(2,2),(2,3),(4,2),(4,3),(4,4),(4,5),(5,3)}(b) R2= {(1,2), (1,3),(1,4),(2,2),(3,3),(5,3),(5,4),(5,2)}IIWhich of them is an equivalence relation?

Any relation is equivalence relation if satisfy the following conditions where is set of elements a)…

Answered: (a) Ri (b) R2= {(1,2),…

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(a) Ri (b) R2= {(1,2), (1,3),(1,4),(2,2),(3,3),(5,3),(5,4),(5,2)} /hich of them is an equivalence relation?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 6TFE: Label each of the following statements as either true or false. Let R be a relation on a nonempty...

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Question

Check if the following relations on the set P = {1,2,3,4,5} are reflexive,
symmetric, antisymmetric and transitive. Justify your answer.
(a) R1 = {(1,1),(1,2),(1,3),(1,5),(2,2),(2,3),(4,2),(4,3),(4,4),(4,5),(5,3)}
(b) R2= {(1,2), (1,3),(1,4),(2,2),(3,3),(5,3),(5,4),(5,2)}
II
Which of them is an equivalence relation?

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