Which of these relations are reflexive? Justify your answers. Which of these relations are symmetric? Justify your answers. Which of these relations are antisymmetric? Justify your answer. d) Which of these relations are transitive? Justify your answers.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 56E
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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)}
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)}
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.
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