Suppose f : A → B is an injective function. Show that there is a function g : B → A such thatg ◦ f = idA. Here, idA : A → A is the identity function on A, i.e., the function that satisfies idA(a) = afor all a ∈ A. (Assume f is non-trivial, i.e., A ̸= ∅!)

An injective function, also known as a one-to-one function, is a type of function in…

Answered: Suppose f : A → B is an injective…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Suppose f : A → B is an injective function. Show that there is a function g : B → A such that
g ◦ f = idA. Here, idA : A → A is the identity function on A, i.e., the function that satisfies idA(a) = a
for all a ∈ A. (Assume f is non-trivial, i.e., A ̸= ∅!)

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