Homework 2

Due Thursday, February 2 at the start of class.

1. Find proofs for the following sequents:
   1. P -> (P -> Q), P |- Q
   2. -P -> -Q, Q |- P
   3. P |- (P -> Q) -> Q
   4. P & (Q & R) |- Q & (P & R)
   5. P & Q |- P v Q
   6. extra credit: -(-P v -Q) |- P & Q
2. Show that the sequent P v Q |- P & Q is unsound, by finding actual propositions for P and Q such that the assumption is true and the conclusion false.