Consider the following arguments. If an argument is valid, then present a proof sequence; otherwise, prove that the argument is invalid. You are forbidden to use truth tables to justify your answers (but, you may use them otherwise).

(a) ((p q) (p q)) q

(b) ((p q) (r q) (r s)) (s p)

(c) ((p (q r)) (r s) (s t)) (t p)