80-211                                                                                                             Spring 2003



Assignment #4

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.