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*)