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~ y iff f(x) = f (y). 5. Let f : X → Y be a surjective function. Define a relation on A by setting x a. Show that is an equivalence relation on X b. Let E be the set of equivalence classes. Show that there is a bijection from E to Y.

~ y iff f(x) = f (y). 5. Let f : X → Y be a surjective function. Define a relation on A by setting x a. Show that is an equivalence relation on X b. Let E be the set of equivalence classes. Show that there is a bijection from E to 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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5. Let f : X → Y be a surjective function. Define a relation on A by setting x - y iff f(x) = f(y). a. Show that is an equivalence relation on X b. Let E be the set of equivalence classes. Show that there is a bijection from E to Y.
Transcribed Image Text:5. Let f : X → Y be a surjective function. Define a relation on A by setting x - y iff f(x) = f(y). a. Show that is an equivalence relation on X b. Let E be the set of equivalence classes. Show that there is a bijection from E to Y.
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