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Problem 5: Another student has started a proof of the proposition Vn E Z where n> 4,n! > 2", and has written their basis step (shown below). Is this a valid basis step? Explain why or why not. Also, how many base cases would be necessary (minimally) for a proof of this proposition? Proof : WTS: Vn e Z where n>4, n! > 2" Step 1: Base Case WTS: P(5) is true . LHS: 5! = 120. RHS: 25 = 32. LHS > RHS. So P(5) is true . WTS: P(6) is true . LHS: 6! = 720. RHS: 26 = 64. LHS > RHS. So P(6) is true . WTS: P(7) is true . LHS: 7! = 5040. RHS: 27 = 128. LHS > RHS. So P(7) is true .

Problem 5: Another student has started a proof of the proposition Vn E Z where n> 4,n! > 2", and has written their basis step (shown below). Is this a valid basis step? Explain why or why not. Also, how many base cases would be necessary (minimally) for a proof of this proposition? Proof : WTS: Vn e Z where n>4, n! > 2" Step 1: Base Case WTS: P(5) is true . LHS: 5! = 120. RHS: 25 = 32. LHS > RHS. So P(5) is true . WTS: P(6) is true . LHS: 6! = 720. RHS: 26 = 64. LHS > RHS. So P(6) is true . WTS: P(7) is true . LHS: 7! = 5040. RHS: 27 = 128. LHS > RHS. So P(7) is true .

Advanced Engineering Mathematics
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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Problem 5: Another student has started a proof of the proposition Vn e Z where n> 4, n! > 2", and has written their basis step (shown below). Is this a valid basis step? Explain why or why not. Also, how many base cases would be necessary (minimally) for a proof of this proposition? Proof : WTS: Vn e Z where n > 4, n! > 2" Step 1: Base Case WTS: P(5) is true . LHS: 5! = 120. RHS: 25 = 32. LHS > RHS. So P(5) is true . WTS: P(6) is true . LHS: 6! = 720. RHS: 26 = 64. LHS > RHS.So P(6) is true . WTS: P(7) is true . LHS: 7! = 5040. RHS: 27 = 128. LHS > RHS. So P(7) is true .
Transcribed Image Text:Problem 5: Another student has started a proof of the proposition Vn e Z where n> 4, n! > 2", and has written their basis step (shown below). Is this a valid basis step? Explain why or why not. Also, how many base cases would be necessary (minimally) for a proof of this proposition? Proof : WTS: Vn e Z where n > 4, n! > 2" Step 1: Base Case WTS: P(5) is true . LHS: 5! = 120. RHS: 25 = 32. LHS > RHS. So P(5) is true . WTS: P(6) is true . LHS: 6! = 720. RHS: 26 = 64. LHS > RHS.So P(6) is true . WTS: P(7) is true . LHS: 7! = 5040. RHS: 27 = 128. LHS > RHS. So P(7) is true .
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