4. Analyze the proof of the theorem and mention one rule of inference used in the proof. Theorem Let nE N. If 7n + 6 is odd then n is odd. Proof Let us assume that n is not odd, that is, n is even. Then we have that n = 2k for some k E N. So 7n + 6 = 7(2k) + 6 = 2 (7k) + 6 = 2 (7k + 3) From here we conclude that 7n + 6 is even in contradiction with the premise of the theorem. Therefore, if 7n 6 is odd then n must be odd