Please Solve The problem in a clear and understandable post. Let A be a finite set, and suppose that f : A → A is one-to-one. Does f necessarilyhave to be onto? Prove or give a counterexample.

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Answered: Let A be a finite set, an« have to be…

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Let A be a finite set, an« have to be onto2 Prove

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.3: Properties Of Composite Mappings (optional)

Problem 12E: Let f:AB and g:BA. Prove that f is one-to-one and onto if fg is one to-one and gf onto.

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Please Solve The problem in a clear and understandable post.

Let A be a finite set, and suppose that f : A → A is one-to-one. Does f necessarily
have to be onto? Prove or give a counterexample.

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