Consider following relations on the set of positive integer: R₁ = {(a,b) | a> b} R₂ = {(a,b) | a = b + 3} R3 = {(a,b) | a+b>4} a) Which of these relations are symmetric and why? If not symmetric give counter example. b) Which of these relations are reflexive and why? If not symmetric give counter example.

Consider following relations on the set of positive integer: R₁ = {(a,b) | a> b} R₂ = {(a,b) | a = b + 3} R3 = {(a,b) | a+b>4} a) Which of these relations are symmetric and why? If not symmetric give counter example. b) Which of these relations are reflexive and why? If not symmetric give counter example.

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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