(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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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
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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