12. Consider the following relations on {1, 2, 3, 4). R1 = {(2,2), (2,31.2,4).(3,2).(3,3).(3,4)} R2 = {(1,1L(1,2).(2,1).(2.2).(3,3).(4,4)} Rs = {2,4lal4,2)} R4 = {(1,21,(2,3).(3,4)} Rs = {(1,1L(2,2),(3,3).(4,4)} a) Which of these relations are reflexive? Justify your answers. b) 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), (2,31.2,4).(3,2).(3,3).(3,4)} R2 = {(1,1L(1,2).(2,1).(2.2).(3,3).(4,4)} Rs = {2,4lal4,2)} R4 = {(1,21,(2,3).(3,4)} Rs = {(1,1L(2,2),(3,3).(4,4)} a) Which of these relations are reflexive? Justify your answers. b) 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.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 14E: In each of the following parts, a relation is defined on the set of all human beings. Determine...
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