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Let A, B and C be nonempty sets and let f : A → B, g: BC and h: B → C be functions. For each of the following, prove or disprove: (a) If f is bijective and go f = hof, then g = h. (b) If gof=hof, then g = h.

Let A, B and C be nonempty sets and let f : A → B, g: BC and h: B → C be functions. For each of the following, prove or disprove: (a) If f is bijective and go f = hof, then g = h. (b) If gof=hof, then g = h.

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 Statement:** Let \( A \), \( B \), and \( C \) be nonempty sets and let \( f: A \to B \), \( g: B \to C \), and \( h: B \to C \) be functions. For each of the following, prove or disprove: (a) If \( f \) is bijective and \( g \circ f = h \circ f \), then \( g = h \). (b) If \( g \circ f = h \circ f \), then \( g = h \).
Transcribed Image Text:**Problem Statement:** Let \( A \), \( B \), and \( C \) be nonempty sets and let \( f: A \to B \), \( g: B \to C \), and \( h: B \to C \) be functions. For each of the following, prove or disprove: (a) If \( f \) is bijective and \( g \circ f = h \circ f \), then \( g = h \). (b) If \( g \circ f = h \circ f \), then \( g = h \).
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