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1. Let X = {z €R:r#0,1} and define f : X X by f(r) = 1-. Prove or disprove that f is a permutation of X. 2. Define f: Z. + 7a by flz) 3(mod 5), Prove or disprove that f is a nermutation of 7.

1. Let X = {z €R:r#0,1} and define f : X X by f(r) = 1-. Prove or disprove that f is a permutation of X. 2. Define f: Z. + 7a by flz) 3(mod 5), Prove or disprove that f is a nermutation of 7.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.3: Factorization In F [x]
Problem 23E: Let f(x),g(x),h(x)F[x] where f(x) and g(x) are relatively prime. If h(x)f(x), prove that h(x) and...
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1. Let X = {z €R:r+0,1} and define f : X X by f(r) 1-. Prove or disprove that f is a permutation of X. 2. Define f: Zg Zg by f(r) = x* (mod 5). Prove or disprove that f is a permutation of Zg.
Transcribed Image Text:1. Let X = {z €R:r+0,1} and define f : X X by f(r) 1-. Prove or disprove that f is a permutation of X. 2. Define f: Zg Zg by f(r) = x* (mod 5). Prove or disprove that f is a permutation of Zg.
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