Please explain each property (withs #'s) 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: Is this binary relation reflexive symmetric antisymmetric transitive |x - y = if x-y 20 ifx-y<0. xRy if x - y < 1. For each of these properties provide a justification why it is satisfied or a counterexample why not.
Please explain each property (withs #'s) 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: Is this binary relation reflexive symmetric antisymmetric transitive |x - y = if x-y 20 ifx-y<0. xRy if x - y < 1. For each of these properties provide a justification why it is satisfied or a counterexample why not.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Please explain each property (withs #'s)
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:
Is this binary relation
reflexive
symmetric
antisymmetric
transitive
|x - y =
if x-y 20
ifx-y<0.
xRy if x - y < 1.
For each of these properties provide a justification why it is satisfied or a counterexample
why not.
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