Let R be a relation on the set of all integers such that aRb if and only if 3a – 5b is ev 1) Is R reflexive? If yes, justify your answer; if no, give a counterexample. 2) Is R symmetric? If yes, justify your answer; if no, give a counterexample. Hint: 3b – 5a = 3a – 5b + 8b – 8a 3) Is R anti-symmetric? If yes, justify your answer; if no, give a counterexample.

Let R be a relation on the set of all integers such that aRb if and only if 3a – 5b is ev 1) Is R reflexive? If yes, justify your answer; if no, give a counterexample. 2) Is R symmetric? If yes, justify your answer; if no, give a counterexample. Hint: 3b – 5a = 3a – 5b + 8b – 8a 3) Is R anti-symmetric? If yes, justify your answer; if no, give a counterexample.

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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