Q3. Let R be a relation on the set A = {1,2,3}, defined as follows: R = {(1,1), (1,2), (1,3), (2, 2), (2, 3), (3, 3), } Which one of the following statements is true? Only 1 statement is true. A. R is reflexive, antisymmetric, and transitive, but R is not symmetric. B. R is reflexive and symmetric, but R is not antisymmetric nor transitive. C. R antisymmetric and transitive, but R is not reflexive nor symmetric. D. R is reflexive, symmetric, and antisymmetric, but R is not transitive. E. R is an equivalence relation on A.

Q3. Let R be a relation on the set A = {1,2,3}, defined as follows: R = {(1,1), (1,2), (1,3), (2, 2), (2, 3), (3, 3), } Which one of the following statements is true? Only 1 statement is true. A. R is reflexive, antisymmetric, and transitive, but R is not symmetric. B. R is reflexive and symmetric, but R is not antisymmetric nor transitive. C. R antisymmetric and transitive, but R is not reflexive nor symmetric. D. R is reflexive, symmetric, and antisymmetric, but R is not transitive. E. R is an equivalence relation on A.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 14E: In each of the following parts, a relation is defined on the set of all human beings. Determine...

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