Define the following relations on A = {5, 6, 7, 9). Answer each of the following questions by listing the index of the relation. For example, for Part 1), if R₁ andR₂ are reflexive, simply enter 1, 2 as the answer.Ro= {(5,5), (7,7), (9,9), (6,6)}R₁ = {(5,5), (7,6), (7, 7), (7, 9), (9, 6), (6, 6), (9,9)}R2 = {(9,9), (7,7), (6, 9), (5, 5), (6, 6), (9,5), (9,6)}R3 = {(7,9), (5,5), (6, 6), (7, 7), (9,9)}R₁ = {(9,9), (5,5), (5,9), (7, 9), (7,5), (6, 6), (9,5), (7, 7), (5,7)}1) Which relations are reflexive?2) Which relations are symmetric?3) Which relations are anti-symmetric?4) Which relations are transitive?

Since you have posted a question with multiple subparts, so we will solve only the first three…

Define the following relations on A = {5,6,7,9). 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= {(5,5), (7,7), (9,9), (6,6)} R₁ = {(5,5), (7,6), (7, 7), (7, 9), (9, 6), (6, 6), (9,9)} R₂ = {(9,9), (7, 7), (6, 9), (5, 5), (6, 6), (9,5), (9,6)} R3 = {(7,9), (5,5), (6, 6), (7, 7), (9,9)} RA= {(9,9), (5,5), (5,9), (7, 9), (7,5), (6, 6), (9,5), (7,7), (5,7)} 1) Which relations are reflexive? 2) Which relations are symmetric? 3) Which relations are anti-symmetric?

Define the following relations on A = {5,6,7,9). 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= {(5,5), (7,7), (9,9), (6,6)} R₁ = {(5,5), (7,6), (7, 7), (7, 9), (9, 6), (6, 6), (9,9)} R₂ = {(9,9), (7, 7), (6, 9), (5, 5), (6, 6), (9,5), (9,6)} R3 = {(7,9), (5,5), (6, 6), (7, 7), (9,9)} RA= {(9,9), (5,5), (5,9), (7, 9), (7,5), (6, 6), (9,5), (7,7), (5,7)} 1) Which relations are reflexive? 2) Which relations are symmetric? 3) Which relations are anti-symmetric?

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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