Which of the following relations on the set {1,2.3,4} are reflexive, symmetric and transitive? R1 = {(1,1), (1,2), (2,1), (2,2), (3,4), (4,1),(4,4)} R2 = {(1,1), (1,2), (1,4), (2,1), (2,2), (3,3), (4,1),(4,4)} R3 = {(1,1), (1,2), (1,3), (1,4), (2,2), (2,3), (2,4), (3,3), (3,4),(4,4)}

Which of the following relations on the set {1,2.3,4} are reflexive, symmetric and transitive? R1 = {(1,1), (1,2), (2,1), (2,2), (3,4), (4,1),(4,4)} R2 = {(1,1), (1,2), (1,4), (2,1), (2,2), (3,3), (4,1),(4,4)} R3 = {(1,1), (1,2), (1,3), (1,4), (2,2), (2,3), (2,4), (3,3), (3,4),(4,4)}

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 1E: For determine which of the following relations onare mappings from to, and justify your answer. ...

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Question

Which of the following relations on the set {1,2.3,4} are reflexive, symmetric and transitive?
R₁ = {(1,1), (1,2), (2,1), (2,2), (3,4), (4,1),(4,4)}
R₂ = {(1,1), (1,2), (1,4), (2,1), (2,2), (3,3), (4,1),(4,4)}
R₃ = {(1,1), (1,2), (1,3), (1,4), (2,2), (2,3), (2,4), (3,3), (3,4),(4,4)}

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