Answered: Let A, B, and C be three sets, and let…

Let A, B, and C be three sets, and let f : A → B and g : B → C be two functions. Assume that the function g ◦ f : A → C is one-to-one. Prove that f is one-to-one.

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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Let A, B, and C be three sets, and let f : A → B and g : B → C be two functions. Assume that the function g ◦ f : A → C is one-to-one. Prove that f is one-to-one.

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