For each of the premise-conclusion pairs below, give a valid step-by-step argument (proof) along with the name of the inference rule used in each step:
(a) Premise: {¬p ∨ q → r, s ∨ ¬q, ¬t, p → t, ¬p ∧ r → ¬s}, conclusion: ¬q.
(b) Premise: {¬p → r ^ ¬s, t → s, u → ¬p, ¬w, u v w}, conclusion: ¬t v w.