What is wrong with the following \"proof\"? Show that \"ail horses are the same

Question

What is wrong with the following "proof"? Show that "ail horses are the same color". Let P(n) = a set of n horses being the same color Basis step: P(1) is true because one horse is the same color Assume P(k) is true, i.e.. all the horses in any set of k horses are the same color Show that P(k + 1) is true: Let h_1, h_2, ... h_k, h_k + 1 be k + 1 horses in a set By inductive hypothesis {h_1, h_2, ...h_k} has the same color and {h_2, h_3, ... H_k + 1} have the same color. Therefore {h_1, h_2, ..., h_k+1} has the same color.

Explanation / Answer

{h2, h3, ... ,hk+1} this given statement is not valid for k=1.

If we take k=1:

P(1) is true

P(k) is true assumption which is again P(1)

P(k+1) => P(2) ... value of k is 1

So, by inductive hypothesis there is not any proof of {h1} and {h2} has same color.

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