Please explain this question with thurough steps as I am having a difficult time grasping the concept. Thank you and Happy holidays! 2. Consider the following relations on the set of integers:R1 = {(a, b) | a < b},R2 = {(a, b) | a > b},R3 = {(a, b) | a = b or a = -b},R4 = {(a, b) | a = b},R5 = {(a, b) | a = b+1},= {(a, b) | a + b < 3}.R6a. Which of the relations contain each of the pairs (1,1), (1,2), (2,1), (1,–1), and(2,2)?b. Which of the relations are reflexive?c. Which of the relations are symmetric?d. Which of the relations are transitive?

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2. Consider the following relations on the set of integers: R1 = {(a, b) | a < b}, R2 = {(a, b) | a > b}, R3 = {(a, b) | a = b or a = –b}, R4 = {(a, b) | a = b}, R5 = {(a, b) | a = b+ 1}, R6 = {(a, b) | a +b < 3}. %3D a. Which of the relations contain each of the pairs (1,1), (1,2), (2,1), (1,–1), and (2,2)? b. Which of the relations are reflexive? c. Which of the relations are symmetric? d. Which of the relations are transitive?

2. Consider the following relations on the set of integers: R1 = {(a, b) | a < b}, R2 = {(a, b) | a > b}, R3 = {(a, b) | a = b or a = –b}, R4 = {(a, b) | a = b}, R5 = {(a, b) | a = b+ 1}, R6 = {(a, b) | a +b < 3}. %3D a. Which of the relations contain each of the pairs (1,1), (1,2), (2,1), (1,–1), and (2,2)? b. Which of the relations are reflexive? c. Which of the relations are symmetric? d. Which of the relations are transitive?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...

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