Let A = {a, b, c}. a) Give an example of a relation on A that is reflexive and symmetric, but is not transitive. b) Give an example of a relation on A that is reflexive and transitive, but is neither symmetric nor antisymmetric. c) Give an example of a relation on A that is antisymmetric and transitive, but is not reflexive.
Let A = {a, b, c}. a) Give an example of a relation on A that is reflexive and symmetric, but is not transitive. b) Give an example of a relation on A that is reflexive and transitive, but is neither symmetric nor antisymmetric. c) Give an example of a relation on A that is antisymmetric and transitive, but is not reflexive.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 20E: Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not...
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