Homework 1

Due Thursday, January 26 at the start of class.

1. Express in symbols the logical form of each sentence of the following argument; write the argument as a sequent.

   If I wash my car, then it will rain.
   
   If it will rain, then I will stay inside and not wash my car.
   
   Therefore, I will not wash my car.
   

2. Fill in the missing pieces of the following proof:

   Q -> (P -> R), -R, Q |- -P
       1 (1) Q -> (P -> R)    __
       2 (2) __                A
      __ (3) Q                 A
      __ (4) P -> R           __
      __ (5) __          2,4 MTT
   

3. Show that the sequent P -> Q |- Q -> P is an unsound pattern of argument by finding actual propositions for P and Q such that the assumption is true but the conclusion is false.
4. Find a proof for the sequent P -> Q, Q -> R |- P -> R.