Exercise 0.3.10: Let f : A –→ B and g: B –→ C be functions. a) Prove that if gof is injective, then f is injective. b) Prove that if gof is surjective, then is surjective. c) Find an explicit example where gof is bijective, but neither f nor g is bijective.
Exercise 0.3.10: Let f : A –→ B and g: B –→ C be functions. a) Prove that if gof is injective, then f is injective. b) Prove that if gof is surjective, then is surjective. c) Find an explicit example where gof is bijective, but neither f nor g is bijective.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.2: Mappings
Problem 27E: 27. Let , where and are nonempty. Prove that has the property that for every subset of if and...
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