Question 1. Find the mistake in the following proof by induction. Claim: Every nonnegative integer is even. Proof: Let P(n) be the statement that n is even. We will use strong induction to prove that P(n) is true for all nonnegative integers n. The base case is n = 0, which is clearly an even number. Thus P(0) is true. Assume that P(n) has been proven for all integers 0 n k. We must prove that k + 1 is even. But by P(1) and P(k), we know that 1 and k are even, hence so is their sum k + 1. Thus P(k + 1) is true. In conclusion, we have proven that n is even for all nonnegative integers n, as required.