Problem 3 please ! Justily yuuI aIS WeI.3. (i) Let F be the collection of all functions f: {0, 1} → N. Is F countable ?(ii) Let F be the collection of all functions f : N {0, 1}. Is F countable ?(iii) Let F be the collection of all functions f : N→ N. Is F countable ? What about f : R → R ?how that |(0, 1)| = |R+| by finding an explicit bijection.

Answered: Image /qna-images/answer/a710c15b-30fd-4abd-b814-a60e911a878a.jpg

Answered: Jus 3. (i) (іi) L- (iii) L

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 21E: Describe the kernel of epimorphism in Exercise 20. Consider the mapping :Z[ x ]Zk[ x ] defined by...

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Describe the kernel of epimorphism in Exercise 20. Consider the mapping :Z[ x ]Zk[ x ] defined by (a0+a1x++anxn)=[ a0 ]+[ a1 ]x++[ an ]xn, where [ ai ] denotes the congruence class of Zk that contains ai. Prove that is an epimorphism from Z[ x ] to Zk[ x ].

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