Discrete mathematics: Please provide an explanation for your solution, as well.

4. Quickly Erupting Diatribe (18 points) (a) [8 Points] Write a formal proof using inference rules of (p) A (r-+ -q))(rp) (b) [1O Points] Write a formal proof using inference rules that, given r -(s^p), s r, and p q, the a^-b) v (-a^b), proposition s q must also be true. You may use the additional equivalence ab which we will call "Definition of e