80-211 Spring 2003

Assignment #3

Due on Friday,
February, 7^{th} .

**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 John’s car is in the garage or Sally took the
car to go the movies.

If John’s 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).