This problem asks you to simplify some recursively defined boolean formulas as much as possible. In each case, prove that your answer is correct. Each proof can be just a few sentences long, but it must be a proof. (a) Suppose ao p, a = q, and an = (an-2 ^ an-1) for all n 2. Simplify an as much as possible. [Hint: What is as?] - (b) Suppose Bo=p, 31= q, and n = (n-2 Bn-1) for all n 2. Simplify n as much as possible. [Hint: What is ?] (e) Suppose yo = P, Y1 =q, and n = (-2n-1) for all n 2. Simplify n as much as possible. (Hint: What is ys?]