Exercise 17.5.20. (a) Show that there is a well-defined function f: Z12 → Z₁, given by f([a]12) = [a]4. That is, show that if [a]12 = [b]12, then [a] = [b]4. 614CHAPTER 17 EQUIVALENCE RELATIONS AND EQUIVALENCE CLASSES (b) Generalize part (a) by showing that if m divides n, then there is a well- defined function f: Zn → Zm, given by f([a]n) = [a]m. That is, show that if [a]n[b]n, then [a]m = [b]m-
Exercise 17.5.20. (a) Show that there is a well-defined function f: Z12 → Z₁, given by f([a]12) = [a]4. That is, show that if [a]12 = [b]12, then [a] = [b]4. 614CHAPTER 17 EQUIVALENCE RELATIONS AND EQUIVALENCE CLASSES (b) Generalize part (a) by showing that if m divides n, then there is a well- defined function f: Zn → Zm, given by f([a]n) = [a]m. That is, show that if [a]n[b]n, then [a]m = [b]m-
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Please do Exercise 17.5.20 part A and B and please show step by step and explain
![Exercise 17.5.20.
(a) Show that there is a well-defined function f: Z12 → Z₁, given by
f([a]12) = [a]4. That is, show that if [a]12 = [b]12, then [a] = [b]4.
614CHAPTER 17 EQUIVALENCE RELATIONS AND EQUIVALENCE CLASSES
(b) Generalize part (a) by showing that if m divides n, then there is a well-
defined function f: Zn → Zm, given by f([a]n) = [a]m. That is, show
that if [a]n[b]n, then [a]m = [b]m-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F892e817a-9b32-4eeb-b8fc-5dd7ffde6479%2F9d2e7c0d-4a43-4b45-a890-ecc4e20bbc96%2Fguzkg9_processed.png&w=3840&q=75)
Transcribed Image Text:Exercise 17.5.20.
(a) Show that there is a well-defined function f: Z12 → Z₁, given by
f([a]12) = [a]4. That is, show that if [a]12 = [b]12, then [a] = [b]4.
614CHAPTER 17 EQUIVALENCE RELATIONS AND EQUIVALENCE CLASSES
(b) Generalize part (a) by showing that if m divides n, then there is a well-
defined function f: Zn → Zm, given by f([a]n) = [a]m. That is, show
that if [a]n[b]n, then [a]m = [b]m-
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