please see the picture ,thanksLet X; Y be two sets. Denote F(X; Y ) the set of all funtions from X to Y . Let A;B ( Xsuch that A [ B = X, A \ B = ;. Show that jF(X; Y )j = jF(A; Y ) F(B; Y )j. 57. Let X,Y be two sets. Denote F(X,Y) the set of all funtions from X to Y. Let A, B C Xsuch that AUB=X, AnB=0. Show that |F(X,Y)| = |F(A,Y) × F(B,Y)|.

Answered: Image /qna-images/answer/a410f962-504a-4a01-9562-fe7f0ccbe62c.jpg

Answered: 5 7. Let X,Y be two sets. Denote F(X,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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Question

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.

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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