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Problem 1 a) Sean A, B, C sets and f: A → B, g: B → Cinvertible functions. Prove yes gof is invertible, so for everything x ECI is true that (go f)-'(x) = (f-1og=')(x) b) Let A, B sets, f : A→Ba function and S A. Consider the following operator: F(S) = {b€ B|3s E S tal que f(s) = b} Show that for everything X, YC A It is true that F(X UY) = F(X)U F(Y)

Problem 1 a) Sean A, B, C sets and f: A → B, g: B → Cinvertible functions. Prove yes gof is invertible, so for everything x ECI is true that (go f)-'(x) = (f-1og=')(x) b) Let A, B sets, f : A→Ba function and S A. Consider the following operator: F(S) = {b€ B|3s E S tal que f(s) = b} Show that for everything X, YC A It is true that F(X UY) = F(X)U F(Y)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 1 a) Sean A, B, Csets and f: A - B, g: B→ Cinvertible functions. Prove yes gof is invertible, so for everything xECIt is true that (g o f)-'(x) = (f-1 og-1)(x) b) Let A, B sets, f: A-Ba function and SCA.Consider the following operator: F(S) = {b € B|3s E S tal que f(s) = b} Show that for everything X, YC A It is true that F(X UY) = F(X)U F(Y)
Transcribed Image Text:Problem 1 a) Sean A, B, Csets and f: A - B, g: B→ Cinvertible functions. Prove yes gof is invertible, so for everything xECIt is true that (g o f)-'(x) = (f-1 og-1)(x) b) Let A, B sets, f: A-Ba function and SCA.Consider the following operator: F(S) = {b € B|3s E S tal que f(s) = b} Show that for everything X, YC A It is true that F(X UY) = F(X)U F(Y)
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