Problem 4 Given the propositions over the natural numbers: p : n n c) P(n, k + 1) = (n - k)P(n, k), a recursive relationship about k-permutations. Hint: the recursive step goes from k to k + 1. Explain your solution (premises, axioms and theorems you used) and write all your work to get full credit. Solution [Write here your solution ....] Problem 6 Let C(x) be the proposition "r is a car". Let V(x) be "x is a vehicle." a) Translate into a formula: every car is a vehicle. b) Assume the proposition from part a) is true. Translate into English: (3x) (-V(x) A C(x)). Is this a tautology or a contradiction? Prove your answer. Explain your solution (premises, axioms and theorems you used) and write all your work to get full credit. Solution [Write here your solution ....]