80-211†††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† ††††††††††† Spring 2003

 

 

Assignment #3

Due on Friday, February, 7th .

 

 

 

1. Do problem 2-(e) on page 33 of your book.

 

2.Find proofs for problems (d), (f), (g), and (i) in the book on page 41.

Note: Be sure to give two proofs (one for each direction) of the sequents that are interderivable, they will be worth 2 points each.

 

3. For the following argument in English, translate it into the propositional calculus and then prove it.

 

Either Johnís car is in the garage or Sally took the car to go the movies.

If Johnís car is in the garage, then Peter must wax the car.

If it is not the case that Peter must wax, then Sally did not take the car to the movies.

Therefore: Peter must wax the car.

 

4. For the formula below do (a) and (b)

††††††††††† (((P→Q) v (Q→S))→(P→S))

 

(a) State which connective is the main connective.

(b) Give an argument using the concepts on pages 42-49 that it is a wff (Suggestion: build a tree to show that it is a wff).