I believe the proposition is incorrect, but I don\'t know what to do for a count

Question

I believe the proposition is incorrect, but I don't know what to do for a counterexample and what part of the proof is wrong

Evaluation of proofs This type of exercise will appear frequently in the book. In each case, there is a proposed proof of a proposition. However, the proposition may be true or may be false If a proposition is false, the proposed proof is, of course, incorrect. In this situation, you are to find the error in the proof and then provide a counterexample showing that the proposition is false. If a proposition is true, the proposed proof may still be incorrect. In this case, you are to determine why the proof is incorrect and then write a correct proof using the writing guidelines that have been presented in this book. If a proposition is true and the proof is correct, you are to decide if the proof is well written or not. If it is well written, then you simply must indicate that this is an excellent proof and needs no revision. On the other hand, if the proof is not well written, then you must then revise the proof so by writing it according to the guidelines presented in this text THis is the proof to be answered based on the directions in the pictures above this. Please provide a correct proof if needed. Also, explain why it is wrong or right.

Explanation / Answer

The proposition is incorrect as we know all dogs are not same breed.

So the base case with just one dog is not correct. It fails when we try to prove it for k+1 assuming it is true for some k>=1

BEcause for k=1 the proof for P(k+1) does not hold because if you have only two dogs then the proof does not work

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