Final version released: Feb 9
You may use any of the rules of inference, including reductio ad absurdum, to prove the following sequents.
(P∧Q) → ¬Q ⊢ P → ¬Q
¬(P→Q) ⊢ P
¬(P→Q) ⊢ Q → R
P → Q ⊢ ¬P ∨ Q
(P∧¬P) ∨ Q ⊢ Q
P → (Q∨R) ⊢ ¬R → (P→Q)