80-211 Spring 2003

Homework #1

Due on Friday,
January 24^{th}.

1. Complete the following sentence: “A pattern of
argument is invalid* *whenever…”

2. Show that the following sequents are invalid patterns of argument by finding actual propositions for P and Q such that the assumptions are true and the conclusion is false.

(a) P® Q, Q ├ P

(b) P® ~Q , ~P ├ Q

3. Explain why the strategy used to show the invalidity of the sequents in problem 2 cannot be used to show validity.

4. Prove the following sequents using rules A, MPP, MTT, DN and CP:

(a) P→ ~ ~Q, P ├ Q

(b) P → Q ├ ~Q → ~P

(c) P→Q, Q→R ├ P→ R

(d) P→(Q→R) ├
(P→Q)→(P→R)

(e) P ├
(P→Q)→Q

(f) ~P ├
(~(Q→R)→P) → (~R→~Q)