Find error in induction proof

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 2 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 Hi with just k horses. By the induction hypothesis, all the horses in Hi 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