Let f: X - Y and g : Y - X be maps between sets. Suppose that g•f is equal to the identity map idy : X - X. Does it follow that f•g is equal to the identity map idy : Y Y? Give a proof or a counterexample.
Let f: X - Y and g : Y - X be maps between sets. Suppose that g•f is equal to the identity map idy : X - X. Does it follow that f•g is equal to the identity map idy : Y Y? Give a proof or a counterexample.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.5: Permutations And Inverses
Problem 10E: 10. Let and be mappings from to. Prove that if is invertible, then is onto and is...
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