Recall that for x, y ≤ R, |x − y| ≤ R is the absolute value of x - y. That is, if x-y>0 ifx-y<0. x-y -(x-y) efine the binary relation R on R as follows: this binary relation reflexive symmetric antisymmetric transitive |x − y| = xRy if |xy| < 1. or each of these properties provide a justification why it is satisfied or a counterexample hy not.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Recall that for x, y ≤ R, |x − y| ≤ R is the absolute value of x - y. That is,
[x - y
| -(x - y)
Define the binary relation R on R as follows:
1
Is this binary relation
reflexive
1 symmetric
antisymmetric
transitive
|x - y =
if x-y>0
if x-y<0.
xRy if |xy| < 1.
For each of these properties provide a justification why it is satisfied or a counterexample
why not.
Transcribed Image Text:Recall that for x, y ≤ R, |x − y| ≤ R is the absolute value of x - y. That is, [x - y | -(x - y) Define the binary relation R on R as follows: 1 Is this binary relation reflexive 1 symmetric antisymmetric transitive |x - y = if x-y>0 if x-y<0. xRy if |xy| < 1. For each of these properties provide a justification why it is satisfied or a counterexample why not.
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