Let f : A → B and g : B –→ C be functions.(a) Prove that if gof is one-to-one, then f is one-to-one.(b) Prove that if go f is onto, then g is onto.

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Answered: Let f : A → B and g : B –→ C be…

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 f : A → B and g : B –→ C be functions. (a) Prove that if gof is one-to-one, then f is one-to-one. (b) Prove that if go f is onto, then g is onto.