80-211                                                                                                             Spring 2003



Homework #1

Due on Friday, January 24th.



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)