empty so is F(X,Y) and |F(X,Y)| = |Y|X| In the next problem you are going to prove this. 5. Problem Base Case State and prove the base case. Inductive Proposition State the inductive proposition Proof of Inductive Proposition You are going to prove the inductive proposition by putting the following steps together A Assume |A| = n implies |P(A)| = 2\4| and let |X| = n + 1. the set X is non- empty. Choose an r € X and let A = X – {r}. Characterize the elements of P(X) – P(A). Denote P(X) – P(A) by Q. B The is an obvious function y: P(A) → Q. Define this function. The function y has an inverse e. Define e and show that it is inverse to 7. State the result that shows |A| = |Q| C Now prove the inductive Proposition.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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empty
so is F(X,Y) and
|F(X,Y)| = |Y|X|
In the next problem you are going to prove this.
5. Problem
Base Case State and prove the base case.
Inductive Proposition State the inductive proposition
Proof of Inductive Proposition You are going to prove the inductive proposition
by putting the following steps together
A Assume |A| = n implies |P(A)| = 2\4| and let |X| = n + 1. the set X is non-
empty. Choose an r € X and let A = X – {r}. Characterize the elements of
P(X) – P(A). Denote P(X) – P(A) by Q.
B The is an obvious function y: P(A) → Q. Define this function.
The function y has an inverse e. Define e and show that it is inverse to 7. State
the result that shows |A| = |Q|
C Now prove the inductive Proposition.
Transcribed Image Text:empty so is F(X,Y) and |F(X,Y)| = |Y|X| In the next problem you are going to prove this. 5. Problem Base Case State and prove the base case. Inductive Proposition State the inductive proposition Proof of Inductive Proposition You are going to prove the inductive proposition by putting the following steps together A Assume |A| = n implies |P(A)| = 2\4| and let |X| = n + 1. the set X is non- empty. Choose an r € X and let A = X – {r}. Characterize the elements of P(X) – P(A). Denote P(X) – P(A) by Q. B The is an obvious function y: P(A) → Q. Define this function. The function y has an inverse e. Define e and show that it is inverse to 7. State the result that shows |A| = |Q| C Now prove the inductive Proposition.
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