80-211 Spring 2003

Assignment #4

Due on Friday,
February, 14^{th} .

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.