Given a function f : A → B, we get a corresponding function f : P(A) → P(B), that maps a subset X ⊆ A to its image f(X) ⊆ B. What condition must f : A → B satisfy for f : P(A) →P(B) to be one-to-one? What condition must f : A → B satisfy for f : P(A) → P(B) to be onto?
Given a function f : A → B, we get a corresponding function f : P(A) → P(B), that maps a subset X ⊆ A to its image f(X) ⊆ B. What condition must f : A → B satisfy for f : P(A) →P(B) to be one-to-one? What condition must f : A → B satisfy for f : P(A) → P(B) to be onto?
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.2: Mappings
Problem 10E: For each of the following parts, give an example of a mapping from E to E that satisfies the given...
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Given a function f : A → B, we get a corresponding function f : P(A) → P(B), that maps a subset X ⊆ A to its image f(X) ⊆ B. What condition must f : A → B satisfy for f : P(A) →P(B) to be one-to-one? What condition must f : A → B satisfy for f : P(A) → P(B) to be onto?
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