Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
0.12 Find the error in the following proof that all horses are the same color. CLAIM: In any set of h horses, all horses are the same color. PROOF: By induction on h. : Basis: For h = 1. In any set containing just one horse, all horses clearly are the same color. Induction step: For k ≥ 1, assume that the claim is true for h = k and prove that it is true for h=k+1. Take any set H of k+ 1 horses. We show that all the horses in this set are the same color. Remove one horse from this set to obtain the set H₁ with just k horses. By the induction hypothesis, all the horses in H₁ are the same color. Now replace the removed horse and remove a different one to obtain the set H₂. By the same argument, all the horses in H₂ are the same color. Therefore, all the horses in H must be the same color, and the proof is complete. 2

0.12 Find the error in the following proof that all horses are the same color. CLAIM: In any set of h horses, all horses are the same color. PROOF: By induction on h. : Basis: For h = 1. In any set containing just one horse, all horses clearly are the same color. Induction step: For k ≥ 1, assume that the claim is true for h = k and prove that it is true for h=k+1. Take any set H of k+ 1 horses. We show that all the horses in this set are the same color. Remove one horse from this set to obtain the set H₁ with just k horses. By the induction hypothesis, all the horses in H₁ are the same color. Now replace the removed horse and remove a different one to obtain the set H₂. By the same argument, all the horses in H₂ are the same color. Therefore, all the horses in H must be the same color, and the proof is complete. 2

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
See similar textbooks
icon
Related questions
Question

Can you help me with this problem because I am having a difficult time trying to figure out how to solve this problem and I don't understand how to do this.

Can you please do this step by step and explain you did it as well.

0.12 Find the error in the following proof that all horses are the same color. CLAIM: In any set of h horses, all horses are the same color. PROOF: By induction on h. : Basis: For h = 1. In any set containing just one horse, all horses clearly are the same color. Induction step: For k ≥ 1, assume that the claim is true for h = k and prove that it is true for h=k+1. Take any set H of k+ 1 horses. We show that all the horses in this set are the same color. Remove one horse from this set to obtain the set H₁ with just k horses. By the induction hypothesis, all the horses in H₁ are the same color. Now replace the removed horse and remove a different one to obtain the set H₂. By the same argument, all the horses in H₂ are the same color. Therefore, all the horses in H must be the same color, and the proof is complete. 2
Transcribed Image Text:0.12 Find the error in the following proof that all horses are the same color. CLAIM: In any set of h horses, all horses are the same color. PROOF: By induction on h. : Basis: For h = 1. In any set containing just one horse, all horses clearly are the same color. Induction step: For k ≥ 1, assume that the claim is true for h = k and prove that it is true for h=k+1. Take any set H of k+ 1 horses. We show that all the horses in this set are the same color. Remove one horse from this set to obtain the set H₁ with just k horses. By the induction hypothesis, all the horses in H₁ are the same color. Now replace the removed horse and remove a different one to obtain the set H₂. By the same argument, all the horses in H₂ are the same color. Therefore, all the horses in H must be the same color, and the proof is complete. 2
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 23 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS