5 7. Let X,Y be two sets. Denote F(X,Y) the set of all funtions from X to Y. Let A, B C X such that AUB=X, AnB=0. Show that |F(X,Y)| = |F(A,Y) × F(B,Y)|.
5 7. Let X,Y be two sets. Denote F(X,Y) the set of all funtions from X to Y. Let A, B C X such that AUB=X, AnB=0. Show that |F(X,Y)| = |F(A,Y) × F(B,Y)|.
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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please see the picture ,thanks
Let X; Y be two sets. Denote F(X; Y ) the set of all funtions from X to Y . Let A;B ( X
such that A [ B = X, A \ B = ;. Show that jF(X; Y )j = jF(A; Y ) F(B; Y )j.

Transcribed Image Text:5
7. Let X,Y be two sets. Denote F(X,Y) the set of all funtions from X to Y. Let A, B C X
such that AUB=X, AnB=0. Show that |F(X,Y)| = |F(A,Y) × F(B,Y)|.
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