For integer n ≥ 1 let P(n) be the predicate that 9 - CEZ. 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+1 = 9.9k - 5.5k - True = = - (95) (9k - 5k) 4(9k – 5k) 4.4c for c EZ by the IH 5n = 4c for some = 4d for d = Z
For integer n ≥ 1 let P(n) be the predicate that 9 - CEZ. 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+1 = 9.9k - 5.5k - True = = - (95) (9k - 5k) 4(9k – 5k) 4.4c for c EZ by the IH 5n = 4c for some = 4d for d = Z
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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True or false?
Transcribed Image Text:For integer n ≥ 1 let P(n) be the predicate that 9 -
CEZ.
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+1 = 9.9k - 5.5k
-
True
=
=
-
(95) (9k - 5k)
4(9k – 5k)
4.4c for c EZ by the IH
5n = 4c for some
= 4d for d = Z
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