Final version: posted Feb 5

A.

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.

1. P → Q ⊢ P → (Q∨R)

2. P → (Q→R) ⊢ Q → (P→R)

3. ¬P ⊢ ¬(P∧Q)

4. ¬(P∨Q) ⊢ ¬P

5. P ⊢ (P→¬P) → ¬P

6. P ⊢ ¬(P→¬P)

B.

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

1. P ∨ (Q∧R) ⊢ P ∨ Q

2. P ∧ (Q∨R) ⊢ (P∧Q) ∨ (P∧R)

3. P ∨ Q, ¬P ⊢ Q

4. (P→R) ∧ (Q→R) ⊢ (P∨Q) → R