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(a) g: Zg → Z6 defined by g(n) = n 2. (b) g: Z6 → Z6 defined by g(x) =x €x. (c) g: Zs → Zs defined by g(n) = n © 2. (d) g: Z11 → Z11 defined by g(n) = n © 2. %3D (e) ga: Z7 → Z, defined by ga(n) = n©a , where a can be any fixed element of Z7.

(a) g: Zg → Z6 defined by g(n) = n 2. (b) g: Z6 → Z6 defined by g(x) =x €x. (c) g: Zs → Zs defined by g(n) = n © 2. (d) g: Z11 → Z11 defined by g(n) = n © 2. %3D (e) ga: Z7 → Z, defined by ga(n) = n©a , where a can be any fixed element of Z7.

Advanced Engineering Mathematics
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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Please do part a, c,e and please show step by step and explain

Exercise 8.3.21. For each function, either prove that it is one-to-one, or prove that it is not. (a) g: Z6 → Z6 defined by g(n) = ne 2. (b) g: Z6 → Z6 defined by g(r) =x €x. (c) g: Zs → Zs defined by g(n) = n© 2. (d) g: Z11 → Z11 defined by g(n) =n© 2. (e) ga: Z7 → Z7 defined by ga(n) = noa , where a can be any fixed element of Z7. (f) fo: Z32 → Z32 defined by fi(n) = nob, be Z32, and b is odd. (g) fb: Ziss → Z18s defined by fi(n) = n ob, be Zıss, and b is even. (h) g: Zs → Zs defined by g(n) = nonon. (i) g: Z7 → Z7 defined by g(n) = nonon.
Transcribed Image Text:Exercise 8.3.21. For each function, either prove that it is one-to-one, or prove that it is not. (a) g: Z6 → Z6 defined by g(n) = ne 2. (b) g: Z6 → Z6 defined by g(r) =x €x. (c) g: Zs → Zs defined by g(n) = n© 2. (d) g: Z11 → Z11 defined by g(n) =n© 2. (e) ga: Z7 → Z7 defined by ga(n) = noa , where a can be any fixed element of Z7. (f) fo: Z32 → Z32 defined by fi(n) = nob, be Z32, and b is odd. (g) fb: Ziss → Z18s defined by fi(n) = n ob, be Zıss, and b is even. (h) g: Zs → Zs defined by g(n) = nonon. (i) g: Z7 → Z7 defined by g(n) = nonon.
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