80-211 Spring 2003
Due on Friday, February, 14th .
1. With just the 10 basic rules prove the following sequent:
(a) ~P→Q ├ P v Q
2. Prove the following sequents using either the 10 basic rules or derived rules (whenever a derived rule is used, the name or number from the book must be given).
(a) P & Q ├ P & (P ↔ Q)
(b) ├ ((P→Q)→P)→P
(c) ~Q ├ P→(Q→R)
(d) (P & Q) → (R v S) ├ (P→R) v (Q → S)
(e) ~(P v Q) v ~(~P v ~Q) ├ P↔Q
(f) ~Q ├ (P v Q)↔P
3. Do problems 1(e), 1(g) and 1(i) on page 73. Be sure to state whether they are tautologous, contingent or inconsistent.