Problem 1 Prove that induction proofs actually works. Mathematically, (P(0) ^ (P(k) = P(k+1))) = P(n) Vn > 0 Hint: contradiction - Problem 2 Show that for any wire whose length is n 2 12, it can be represented as pieces of exactly 4 and 5 units. Hint: Induction

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 63RE
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Please, I need the first prove by contradiction, and the second problem prove by  Induction with well hand write or computer typing

 

Problem 1
Prove that induction proofs actually works. Mathematically,
(P(0) ^ (P(k) → → P(n) Vn 2 0
P(k + 1)))
Hint: contradiction
Problem 2
Show that for any wire whose length is n > 12, it can be represented as pieces of exactly 4 and 5 units.
Hint: Induction
[ ]
Transcribed Image Text:Problem 1 Prove that induction proofs actually works. Mathematically, (P(0) ^ (P(k) → → P(n) Vn 2 0 P(k + 1))) Hint: contradiction Problem 2 Show that for any wire whose length is n > 12, it can be represented as pieces of exactly 4 and 5 units. Hint: Induction [ ]
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