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Define the following relations on A = {0, 1,2, 4}. Answer each of the following questions by listing the index of the relation. For example, for Part 1), if R1 and R2 are reflexive, simply enter 1, 2 as the answer. Ro = {(4,2), (4, 4), (4, 0), (0, 2), (0, 1), (4, 1)} R = {(4,4), (0,0), (1, 1), (2, 2)} R2 = {(4, 4), (2,0), (2, 2), (1,4), (2, 1), (0,0)} R3 = {(2,2), (1,0), (0,0), (1, 1), (0, 1), (4, 4)} R4 {(4, 4), (2,0), (2, 1), (1, 2), (1,4), (4, 1), (0, 2)} 1) Which relations are reflexive? 1 2) Which relations are symmetric? 4 3) Which relations are anti-symmetric? 4) Which relations are transitive? 2

Define the following relations on A = {0, 1,2, 4}. Answer each of the following questions by listing the index of the relation. For example, for Part 1), if R1 and R2 are reflexive, simply enter 1, 2 as the answer. Ro = {(4,2), (4, 4), (4, 0), (0, 2), (0, 1), (4, 1)} R = {(4,4), (0,0), (1, 1), (2, 2)} R2 = {(4, 4), (2,0), (2, 2), (1,4), (2, 1), (0,0)} R3 = {(2,2), (1,0), (0,0), (1, 1), (0, 1), (4, 4)} R4 {(4, 4), (2,0), (2, 1), (1, 2), (1,4), (4, 1), (0, 2)} 1) Which relations are reflexive? 1 2) Which relations are symmetric? 4 3) Which relations are anti-symmetric? 4) Which relations are transitive? 2

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 6TFE: Label each of the following statements as either true or false. Let R be a relation on a nonempty...
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Define the following relations on A = {0, 1,2, 4}. Answer each of the following questions by listing the index of the relation. For example, for Part 1), if R1 and R2 are reflexive, simply enter 1, 2 as the answer. Ro = {(4, 2), (4, 4), (4, 0), (0, 2), (0, 1), (4, 1)} R1 = {(4,4), (0, 0), (1, 1), (2, 2)} R2 = {(4, 4), (2, 0), (2, 2), (1,4), (2, 1), (0,0)} R3 = {(2,2), (1,0), (0,0), (1, 1), (0, 1), (4, 4)} R4 {(4, 4), (2,0), (2, 1), (1, 2), (1,4), (4, 1), (0, 2)} 1) Which relations are reflexive? 1 2) Which relations are symmetric? 4 3) Which relations are anti-symmetric? 3 4) Which relations are transitive? 2
Transcribed Image Text:Define the following relations on A = {0, 1,2, 4}. Answer each of the following questions by listing the index of the relation. For example, for Part 1), if R1 and R2 are reflexive, simply enter 1, 2 as the answer. Ro = {(4, 2), (4, 4), (4, 0), (0, 2), (0, 1), (4, 1)} R1 = {(4,4), (0, 0), (1, 1), (2, 2)} R2 = {(4, 4), (2, 0), (2, 2), (1,4), (2, 1), (0,0)} R3 = {(2,2), (1,0), (0,0), (1, 1), (0, 1), (4, 4)} R4 {(4, 4), (2,0), (2, 1), (1, 2), (1,4), (4, 1), (0, 2)} 1) Which relations are reflexive? 1 2) Which relations are symmetric? 4 3) Which relations are anti-symmetric? 3 4) Which relations are transitive? 2
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