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Let f be a function from X to Y. For A CX, let also f(A) denote the set f(A) = {f(a) | a E A}. Prove that f is one-to-one if and only if f(An B) = f(A)n f(B) for any subsets A, BC X.

Let f be a function from X to Y. For A CX, let also f(A) denote the set f(A) = {f(a) | a E A}. Prove that f is one-to-one if and only if f(An B) = f(A)n f(B) for any subsets A, BC X.

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Let f be a function from X to Y .

For A ⊆ X, let also f(A) denote the set f(A) = {f(a) | a ∈ A}.

Prove that f is one-to-one

if and only if f(A ∩ B) = f(A) ∩ f(B) for any subsets A, B ⊆ X.

Let f be a function from X to Y. For A CX, let also f(A) denote the set f(A) = {f(a) | a E A}. Prove that f is one-to-one if and only if f(An B) = f(A)n f(B) for any subsets A, BC X.
Transcribed Image Text:Let f be a function from X to Y. For A CX, let also f(A) denote the set f(A) = {f(a) | a E A}. Prove that f is one-to-one if and only if f(An B) = f(A)n f(B) for any subsets A, BC X.
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