Which of these relations on {0, 1, 2, 3} are equivalence relations? Determine the properties of an equivalence re- lation that the others lack. a) {(0,0), (1, 1), (2, 2), (3, 3)} b) {(0, 0), (0, 2), (2, 0), (2, 2), (2, 3), (3, 2), (3, 3)} c) {(0,0), (1, 1), (1, 2), (2, 1), (2, 2), (3, 3)} d) {(0, 0), (1, 1), (1, 3), (2, 2), (2, 3), (3, 1), (3, 2), (3,3)} e) {(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 2), (3, 3)}
Which of these relations on {0, 1, 2, 3} are equivalence relations? Determine the properties of an equivalence re- lation that the others lack. a) {(0,0), (1, 1), (2, 2), (3, 3)} b) {(0, 0), (0, 2), (2, 0), (2, 2), (2, 3), (3, 2), (3, 3)} c) {(0,0), (1, 1), (1, 2), (2, 1), (2, 2), (3, 3)} d) {(0, 0), (1, 1), (1, 3), (2, 2), (2, 3), (3, 1), (3, 2), (3,3)} e) {(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 2), (3, 3)}
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
NOTE: This question requires that I find the equivalence classes and not the equivalence relations.
![1. Which of these relations on {0, 1, 2, 3} are equivalence
relations? Determine the properties of an equivalence re-
lation that the others lack.
a) {(0, 0), (1, 1), (2, 2), (3, 3)}
b) {(0, 0), (0, 2), (2, 0), (2, 2), (2, 3), (3, 2), (3, 3)}
c) {(0, 0), (1, 1), (1, 2), (2, 1), (2, 2), (3, 3)}
d) {(0, 0), (1, 1), (1, 3), (2, 2), (2, 3), (3, 1), (3, 2),
(3,3)}
e) {(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0),
(2, 2), (3, 3)}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f8e2f43-d44d-4f21-8136-f62bbb5d88f2%2Fd9f72fe5-4e2b-483b-a351-70b430b884f1%2Fymhpafw_processed.png&w=3840&q=75)
Transcribed Image Text:1. Which of these relations on {0, 1, 2, 3} are equivalence
relations? Determine the properties of an equivalence re-
lation that the others lack.
a) {(0, 0), (1, 1), (2, 2), (3, 3)}
b) {(0, 0), (0, 2), (2, 0), (2, 2), (2, 3), (3, 2), (3, 3)}
c) {(0, 0), (1, 1), (1, 2), (2, 1), (2, 2), (3, 3)}
d) {(0, 0), (1, 1), (1, 3), (2, 2), (2, 3), (3, 1), (3, 2),
(3,3)}
e) {(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0),
(2, 2), (3, 3)}
![26. What are the equivalence classes of the equivalence rela-
tions in Exercise 1?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f8e2f43-d44d-4f21-8136-f62bbb5d88f2%2Fd9f72fe5-4e2b-483b-a351-70b430b884f1%2Fdgs21gi_processed.png&w=3840&q=75)
Transcribed Image Text:26. What are the equivalence classes of the equivalence rela-
tions in Exercise 1?
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