Determine whether eäch o
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Q 9 a,b, c
![8. Determine whether each of the binary relations R definer
on the given sets A is reflexive, symmetric, antisymmet
ric, or transitive. If a relation has a certain property, prove
this is so; otherwise, provide a counterexample to show
that it does not.
(a) [BB] A is the set of all English words; (a, b) ER if
and only if a and b have at least one letter in com-
.2, illustrate a relation on
tric
mon.
(b) A is the set of all people. (a, b) e R if and only
if neither a nor b is currently enrolled at Miskatonic
University or else both are enrolled at MU and are
taking at least one course together.
9. Answer Exercise 8 for each of the following relations:
(a) A = {1, 2}; R = {(1, 2)}.
(b) [BB] A = {1, 2, 3, 4}; R = {(1, 1), (1, 2), (2, 1),
(3,4)}.
(c) [BB] A = Z; (a, b) ER if and only if ab > 0.
(d) A = R; (a, b) ER if and only if a? = b². -7
(e) A = R; (a, b) ER if and only if a -b < 3.
AO A = Z x Z; ((a, b), (c, d)) e R if and only if
a - c = b - d.
(g) A = N; (a, b) ER if and only if a # b.
(h) A = Z; R = {(x, y) | x+y = 10}.
isymmetric
metric
each relation.
ered pairs in a relation on
ametric, and not transitive
netric nor transitive
exive nor transitive
zive nor symmetric
%3D
ut not transitive
not symmetric
ive, but not reflexive
ransitive](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6cafa13c-3723-4a0f-827c-f778a168ea31%2F610698b4-19fd-4d0b-ad9c-5f8c9338337d%2Fstokbgm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:8. Determine whether each of the binary relations R definer
on the given sets A is reflexive, symmetric, antisymmet
ric, or transitive. If a relation has a certain property, prove
this is so; otherwise, provide a counterexample to show
that it does not.
(a) [BB] A is the set of all English words; (a, b) ER if
and only if a and b have at least one letter in com-
.2, illustrate a relation on
tric
mon.
(b) A is the set of all people. (a, b) e R if and only
if neither a nor b is currently enrolled at Miskatonic
University or else both are enrolled at MU and are
taking at least one course together.
9. Answer Exercise 8 for each of the following relations:
(a) A = {1, 2}; R = {(1, 2)}.
(b) [BB] A = {1, 2, 3, 4}; R = {(1, 1), (1, 2), (2, 1),
(3,4)}.
(c) [BB] A = Z; (a, b) ER if and only if ab > 0.
(d) A = R; (a, b) ER if and only if a? = b². -7
(e) A = R; (a, b) ER if and only if a -b < 3.
AO A = Z x Z; ((a, b), (c, d)) e R if and only if
a - c = b - d.
(g) A = N; (a, b) ER if and only if a # b.
(h) A = Z; R = {(x, y) | x+y = 10}.
isymmetric
metric
each relation.
ered pairs in a relation on
ametric, and not transitive
netric nor transitive
exive nor transitive
zive nor symmetric
%3D
ut not transitive
not symmetric
ive, but not reflexive
ransitive
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