Let A, B, C be sets. Let f : A → B and g : B → C be functions. a) Prove that if f and g are bijective, then so is g ◦ f. b) If g ◦ f is bijective, are f and g? Prove or disprove.
Let A, B, C be sets. Let f : A → B and g : B → C be functions. a) Prove that if f and g are bijective, then so is g ◦ f. b) If g ◦ f is bijective, are f and g? Prove or disprove.
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, C be sets. Let f : A → B and g : B → C be functions.
a) Prove that if f and g are bijective, then so is g ◦ f.
b) If g ◦ f is bijective, are f and g? Prove or disprove.
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