This preview shows page 1. Sign up to view the full content.
Unformatted text preview: p p DN It is worth noting that _ I, &O, $ O and DN require only one line for justiFcation, whereas _ O, ! O, &I, and $ I require two. The OUT rules are rules for using statements of a certain form (with a certain main operator). The IN rules are rules for deriving or getting statements of a certain form. With all of these rules in place, we can prove the validity of a wide variety of different arguments. Here are some sample derivations. 1. 2. 3. 4. 5. 6. ( F _ G ) ! ( H & J ) F SHOW: H F _ G H & J H Pr Pr DD 2 _ I 1,4 ! O 5 &O 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. ( A & B ) ! C A D _ C A ! B SHOW: D & B B A & B C D D & B Pr Pr Pr Pr DD 2,4 ! O 2,6 &I 1,7 ! O 3,8 _ O 6,9 &I 4...
View Full Document
This note was uploaded on 11/22/2011 for the course PHIL 110 taught by Professor Bohn during the Spring '08 term at UMass (Amherst).
- Spring '08