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12. Consider the following relations on {1, 2, 3, 4}. R₁ = {(2,2), (2,3), (2,4), (3,2), (3,3), (3,4)} R₂ = {(1,1),(1,2), (2,1),(2,2), (3,3), (4,4)} R3 = {2,4),(4,2)} R4 = {(1,2), (2,3), (3,4)} R5 = {(1,1),(2,2), (3,3), (4,4)}

12. Consider the following relations on {1, 2, 3, 4}. R₁ = {(2,2), (2,3), (2,4), (3,2), (3,3), (3,4)} R₂ = {(1,1),(1,2), (2,1),(2,2), (3,3), (4,4)} R3 = {2,4),(4,2)} R4 = {(1,2), (2,3), (3,4)} R5 = {(1,1),(2,2), (3,3), (4,4)}

Elements Of Modern Algebra
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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a) Which of these relations are reflexive? Justify your answers. Which of these relations are symmetric? Justify your answers. c) Which of these relations are antisymmetric? Justify your answer. d) Which of these relations are transitive? Justify your answers.
Transcribed Image Text:a) Which of these relations are reflexive? Justify your answers. Which of these relations are symmetric? Justify your answers. c) Which of these relations are antisymmetric? Justify your answer. d) Which of these relations are transitive? Justify your answers.
12. Consider the following relations on {1, 2, 3, 4}. R₁ = {(2,2), (2,3), (2,4), (3,2), (3,3), (3,4)} R2= {(1,1),(1,2), (2,1),(2,2), (3,3), (4,4)} R3 = {2,4),(4,2)} R4 = {(1,2), (2,3), (3,4)} Rs = {(1,1),(2,2), (3,3), (4,4)}
Transcribed Image Text:12. Consider the following relations on {1, 2, 3, 4}. R₁ = {(2,2), (2,3), (2,4), (3,2), (3,3), (3,4)} R2= {(1,1),(1,2), (2,1),(2,2), (3,3), (4,4)} R3 = {2,4),(4,2)} R4 = {(1,2), (2,3), (3,4)} Rs = {(1,1),(2,2), (3,3), (4,4)}
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