Determine whether the relation R on the set of all integers is reflexive, symmetric, antisymmetric, and/or transitive, where (x, y) e R if and only if а) х # у. с) х %3D у+1оr x %3D у — 1. d) x = y (mod 7). f) x and y are both negative or both nonnegative. g) x = b) xy > 1. e) x is a multiple of y. h) x > y².
Determine whether the relation R on the set of all integers is reflexive, symmetric, antisymmetric, and/or transitive, where (x, y) e R if and only if а) х # у. с) х %3D у+1оr x %3D у — 1. d) x = y (mod 7). f) x and y are both negative or both nonnegative. g) x = b) xy > 1. e) x is a multiple of y. h) x > y².
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:7. Determine whether the relation R on the set of all integers
is reflexive, symmetric, antisymmetric, and/or transitive,
where (x, y) E R if and only if
а) х + у.
с) х %3D у + 1 or x — у — 1.
d) x = y (mod 7).
f) x and y are both negative or both nonnegative.
g) x = y2.
b) xy > 1.
e) x is a multiple of y.
h) х > у2.
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