(a) x+y=0 A. symmetric B. irreflexive C. antisymmetric D. reflexive E. transitive (b) ay is an integer A. antisymmetric B. transitive C. irreflexive D. reflexive OE. symmetric (C) x = 2y A. symmetric B. reflexive C. irreflexive D. antisymmetric E. transitive (d) ry > 1 A. transitive B. symmetric C. irreflexive D. antisymmetric E. reflexive
(a) x+y=0 A. symmetric B. irreflexive C. antisymmetric D. reflexive E. transitive (b) ay is an integer A. antisymmetric B. transitive C. irreflexive D. reflexive OE. symmetric (C) x = 2y A. symmetric B. reflexive C. irreflexive D. antisymmetric E. transitive (d) ry > 1 A. transitive B. symmetric C. irreflexive D. antisymmetric E. reflexive
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 15E: Let A=R0, the set of all nonzero real numbers, and consider the following relations on AA. Decide in...
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Question
![Given the following relations on the set of all integers where (x, y) = R if and only if the following is satisfied. (Check ALL correct answers from the following lists ):
(a) x+y=0
A. symmetric
B. irreflexive
C. antisymmetric
D. reflexive
E. transitive
(b) ay is an integer
A. antisymmetric
B. transitive
OC. irreflexive
OD. reflexive
OE. symmetric
(C) x = 2y
A. symmetric
B. reflexive
C. irreflexive
OD. antisymmetric
E. transitive
(d) xy > 1
A. transitive
OB. symmetric
C. irreflexive
OD. antisymmetric
E. reflexive](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F142234a2-d1e7-405c-983a-f3b165f54d87%2Febad4a1f-bb94-424c-a0fb-c8fdd613c6a9%2Fat6rzmc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given the following relations on the set of all integers where (x, y) = R if and only if the following is satisfied. (Check ALL correct answers from the following lists ):
(a) x+y=0
A. symmetric
B. irreflexive
C. antisymmetric
D. reflexive
E. transitive
(b) ay is an integer
A. antisymmetric
B. transitive
OC. irreflexive
OD. reflexive
OE. symmetric
(C) x = 2y
A. symmetric
B. reflexive
C. irreflexive
OD. antisymmetric
E. transitive
(d) xy > 1
A. transitive
OB. symmetric
C. irreflexive
OD. antisymmetric
E. reflexive
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