602 CHAPTER 17 EQUIVALENCE RELATIONS AND EQUIVALENCE CLASSES (a) Let B = {1, 2, 3, 4, 5} and S = {(1, 1), (1,4), (2, 2), (2,3), (3,2), (3, 3), (4,1), (4,4), (5,5)}. Assume (without proof) that S is an equivalence relation on B. Find the equivalence class of each element of B. (b) Let C = {1, 2, 3, 4, 5} and define ~ by x~Cyx+y is even. Assume (without proof) that ~ is an equivalence relation on C. Find the equivalence class of each element of C. (c) Draw the arrow diagrams for the relations in R in Example 17.4.5, and for the relations in parts (a) and (b) of this exercise.
602 CHAPTER 17 EQUIVALENCE RELATIONS AND EQUIVALENCE CLASSES (a) Let B = {1, 2, 3, 4, 5} and S = {(1, 1), (1,4), (2, 2), (2,3), (3,2), (3, 3), (4,1), (4,4), (5,5)}. Assume (without proof) that S is an equivalence relation on B. Find the equivalence class of each element of B. (b) Let C = {1, 2, 3, 4, 5} and define ~ by x~Cyx+y is even. Assume (without proof) that ~ is an equivalence relation on C. Find the equivalence class of each element of C. (c) Draw the arrow diagrams for the relations in R in Example 17.4.5, and for the relations in parts (a) and (b) of this exercise.
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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Question
Please do part A,B,C and please show step by step and explain
![Example 17.4.5. Suppose A = {1,2,3,4,5} and
R=
{(1, 1), (1, 3), (1,4), (2, 2), (2, 5), (3, 1), (3, 3), (3, 4), (4, 1), (4, 3), (4,4), (5,2), (5,5)}
One can verify that R is an equivalence relation on A. The equivalence
classes are:
[1] = [3] = [4] = {1,3,4}, [2] = [5] = {2,5}.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F892e817a-9b32-4eeb-b8fc-5dd7ffde6479%2Fa023e8e6-79ab-4788-af9f-06dc731bc32a%2Fxqxlwjw_processed.png&w=3840&q=75)
Transcribed Image Text:Example 17.4.5. Suppose A = {1,2,3,4,5} and
R=
{(1, 1), (1, 3), (1,4), (2, 2), (2, 5), (3, 1), (3, 3), (3, 4), (4, 1), (4, 3), (4,4), (5,2), (5,5)}
One can verify that R is an equivalence relation on A. The equivalence
classes are:
[1] = [3] = [4] = {1,3,4}, [2] = [5] = {2,5}.
Transcribed Image Text:602 CHAPTER 17 EQUIVALENCE RELATIONS AND EQUIVALENCE CLASSES
(a) Let B = {1, 2, 3, 4, 5} and
S = {(1, 1), (1,4), (2, 2), (2,3), (3,2), (3, 3), (4,1), (4,4), (5,5)}.
Assume (without proof) that S is an equivalence relation on B. Find
the equivalence class of each element of B.
(b) Let C = {1, 2, 3, 4, 5} and define ~ by
x~Cyx+y is even.
Assume (without proof) that ~ is an equivalence relation on C. Find
the equivalence class of each element of C.
(c) Draw the arrow diagrams for the relations in R in Example 17.4.5, and
for the relations in parts (a) and (b) of this exercise.
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