Answered: 1. Consider a function f: Z → Z where…

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1. Consider a function f: Z → Z where f(x)= 5x − 13. Prove or disprove f is injective.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 11E: For the given f:ZZ, decide whether f is onto and whether it is one-to-one. Prove that your decisions...

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Question

1. Consider a function f: Z → Z where f(x)= 5x − 13. Prove or disprove f is injective.

2. Let S be a set. Suppose every function f: S → S also has an inverse function f−1. Prove or disprove that |S| must only be 0 or 1.

3.The function f: Z3 → Z denotes a function that maps an ordered tuple onto an integer. Consider such an f(x, y, z) = x + y2 + z2. Prove or disprove that f is surjective.

4.Prove or disprove. Given any set S with any surjective function f: S → S, f must be bijective.

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