Final version: posted Feb 5

Use Conditional Proof (and possibly the previous rules) to prove the following sequents. Be sure to include dependency numbers in the leftmost column of your proof.

*P*→*Q*⊢*P*→ (*Q*∨*R*)*P*→ (*Q*→*R*) ⊢*Q*→ (*P*→*R*)¬

*P*⊢ ¬(*P*∧*Q*)¬(

*P*∨*Q*) ⊢ ¬*P**P*⊢ (*P*→¬*P*) → ¬*P**P*⊢ ¬(*P*→¬*P*)

Use ∨-elimination (and possibly the
previous rules) to prove the following sequents. Do *not* use
reductio ad absurdum for any of these proofs.

*P*∨ (*Q*∧*R*) ⊢*P*∨*Q**P*∧ (*Q*∨*R*) ⊢ (*P*∧*Q*) ∨ (*P*∧*R*)*P*∨*Q*, ¬*P*⊢*Q*(

*P*→*R*) ∧ (*Q*→*R*) ⊢ (*P*∨*Q*) →*R*