Question 2. (12 pts). Alice wants to prove by induction that a predicate P holds for certain nonnegative integers. She has proven that for all nonnegative integers n-0,1,... P(n)P(n +3) (a) Which of the following, ifalso proven true, would enable Alice to conclude Vn 2 5.P(n)? Just answer yes or no. (4 pts) 1. P(5) and P(6) 2. P(O), P1), and P(2) 3. P(2), P(4), and P(5) 4. P(3), P(5), and P(7) (b) Suppose Alice manages to also prove that P(5) holds. Which of the following propositions can she now deduce? Answer yes or no with a one sentence explanation, separately for each part. (8 pts) 1. P(n) holds for all n25. 2. P(3n) holds for alln 25. 3. P(n) holds for n 8,11,14,... 4. P(n) does not hold for any n 2