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April 23, 2014

Homework Help: computer sciece(Computation Theory)

Posted by Alex on Monday, September 26, 2011 at 3:22am.

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 the 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 di erent 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.

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