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Decide whether each

Decide whether each

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.1: Polynomials Over A Ring
Problem 24E
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Decide whether each of the following functions is injective and/or surjective. f : N → N defined by f(n) = n+ 1. Of is injective but not surjective Of is surjective but not injective Of is both injective and surjective Of is neither injective nor surjective. g : R× R f(m, n) = (m + n, m – n). → Rx R defined by Og is injective but not surjective Og is surjective but not injective Og is both injective and surjective Og is neither injective nor surjective. h : N → {0, 1,2, 3, 4, 5, 6, 7, 8, 9} defined by h(n) = the last digit of n². Oh is injective but not surjective Oh is surjective but not injective Oh is both injective and surjective Oh is neither injective nor surjective.
Transcribed Image Text:Decide whether each of the following functions is injective and/or surjective. f : N → N defined by f(n) = n+ 1. Of is injective but not surjective Of is surjective but not injective Of is both injective and surjective Of is neither injective nor surjective. g : R× R f(m, n) = (m + n, m – n). → Rx R defined by Og is injective but not surjective Og is surjective but not injective Og is both injective and surjective Og is neither injective nor surjective. h : N → {0, 1,2, 3, 4, 5, 6, 7, 8, 9} defined by h(n) = the last digit of n². Oh is injective but not surjective Oh is surjective but not injective Oh is both injective and surjective Oh is neither injective nor surjective.
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