(i) [BB] A = R?; R = {((x, y), (u, v)) | x+y
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
Q10
![(i) [BB] A = R?; R = {((x, y), (u, v)) | x+y <u+v}.
(i) A = N; (a, b) e R if and only if is an integer.
(k) A = Z; (a, b) e R if and only if 4 is an integer.
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%3D
%3D
%3D
10. Define R on R by (x, y) € R if and only if 1 <
|x|+lyl < 2.
(a) Make a sketch in the Cartesian plane showing the
region of R2 defined by R.
(b) Show that R is neither reflexive nor transitive.
(c) Is R symmetric? Is it antisymmetric? Explain.
11. Let S be a set that contains at least two elements a and
b. Let A be the power set of S. Determine which
of the properties-reflexivity, symmetry, antisymmetry,
transitivity-each of the following binary relations R on
A possesses. Give a proof or counterexample as appro-
priate](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7a6f4d1-5574-4afc-bfb9-6d15c839bf1a%2Fd5af1339-8e89-473a-94af-966cb6a7482d%2F1fhphcc.jpeg&w=3840&q=75)
Transcribed Image Text:(i) [BB] A = R?; R = {((x, y), (u, v)) | x+y <u+v}.
(i) A = N; (a, b) e R if and only if is an integer.
(k) A = Z; (a, b) e R if and only if 4 is an integer.
%3D
%3D
%3D
%3D
10. Define R on R by (x, y) € R if and only if 1 <
|x|+lyl < 2.
(a) Make a sketch in the Cartesian plane showing the
region of R2 defined by R.
(b) Show that R is neither reflexive nor transitive.
(c) Is R symmetric? Is it antisymmetric? Explain.
11. Let S be a set that contains at least two elements a and
b. Let A be the power set of S. Determine which
of the properties-reflexivity, symmetry, antisymmetry,
transitivity-each of the following binary relations R on
A possesses. Give a proof or counterexample as appro-
priate
Expert Solution
Step 1
Given:
A relation on defined as follows:
if and only if
(a.) To make a sketch in the Cartesian plane showing the region of defined by
(b.) To show that is neither reflexive nor transitive
(c.) To explain and check if is symmetric or anti-symmetric
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