Philosophy 60                                                                  :    
Homework 1

Instructions:  Complete the following problems as directed.  Type your name.  Type your answers. Staple or paper clip multiple pages.  If you turn this in by e-mail, type the date and time you sent it on the hardcopy.   10 pts. total.

Note:  The box in the upper right hand corner is a preformatted textbox.  You can select it for copying and pasting by clicking on the perimeter.  You can expand it to whatever size you need by grabbing it on the perimeter and pulling.   It is useful for both truth trees and natural deduction.

1.  Use a truth tree to determine whether the following argument is valid.  Be sure to state the result (valid or invalid) and explain what part of the truth tree demonstrates this.  (2 pts.)

(p v q); ¬(r →p)  (¬q ↔ ¬s)

2.  Use a truth tree to determine whether the following sentence is a tautology. Explain as above. (2 pts.)

¬(p ↔q) ↔ ((p & ¬q) v ¬(¬¬p v ¬q))

3.  Us a truth tree to determine whether the following is a contradiction.  Explain as above.  (2 pts.)

(p & q) → ¬(p v q)

4.  Prove the following using natural deduction, direct proof method.  (2pts.)

p & ¬¬ q;  (r → s) & t    (¬¬t & q) &  p

5.  Prove the following using natural deduction, indirect proof method.  (2pts.)

(p & s) → ¬( q & r);  (s & t) & p  ¬(r & q)    (2pts.)