For integer n I let P(n) be the predicate that 9" CEZ. = 4c for some For the induction hypothesis, consider k≥ 1, and suppose that P(k) is true. For the inductive step, we want to show that P(k+ 1) is true. True or false: The following proof correctly proves P(k+1) true, where every step other than the one labelled IH follows by algebra. (I'm asking: is this a valid algebraic proof? Is the algebra correct? Did I use the IH correctly? Did I get the correct final result?) 9k+15k+19.9k - 5.5k = 9(4c5k) 5.5k for CEZ by the IH
For integer n I let P(n) be the predicate that 9" CEZ. = 4c for some For the induction hypothesis, consider k≥ 1, and suppose that P(k) is true. For the inductive step, we want to show that P(k+ 1) is true. True or false: The following proof correctly proves P(k+1) true, where every step other than the one labelled IH follows by algebra. (I'm asking: is this a valid algebraic proof? Is the algebra correct? Did I use the IH correctly? Did I get the correct final result?) 9k+15k+19.9k - 5.5k = 9(4c5k) 5.5k for CEZ by the IH
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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
Transcribed Image Text:=
For integer n ≥ 1 let P(n) be the predicate that 9" - 5n
CEZ
4c for some
For the induction hypothesis, consider k ≥ 1, and suppose that P(k) is true.
For the inductive step, we want to show that P(k+1) is true.
True or false: The following proof correctly proves P(k+ 1) true, where every
step other than the one labelled IH follows by algebra. (I'm asking: is this a valid
algebraic proof? Is the algebra correct? Did I use the IH correctly? Did I get the
correct final result?)
9k+15k+19.9k - 5.5k
True
False
= 9(4c – 5k) – 5 ⋅ 5% for CE Z by the IH
= 4.9c-9.5k - 5.5k
= 4.9c-4.5k
= 4d for d = Z
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