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ln2-page5 - 1 2 3 4 5(S T U W U Pr T Pr S W K SHOW K Pr S!T...

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1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. ( S ! T ) ( U _ W ) T U ( S W ) ! K SHOW: K S ! T U _ W S W S W K Pr Pr Pr Pr DD 2,6 ! O 3,7 _ O 4,10 ! O 1. 2. 3. 4. 5. 6. 7. D ! ( F ! E ) ( E ! F ) _ D D SHOW: E $ F F ! E E ! F E $ F Pr Pr Pr DD 1,3 ! O 2,3 _ O 5,6 $ I These next examples show that DN is often used to set up ! O or _ O: 1. 2. 3. 4. 5. 6. 7. 8. ( P $ Q ) _⇠ R R Q SHOW: P ⇠⇠ R P $ Q Q ! P P Pr Pr Pr DD 2 DN 1,5 _ O 6 $ O 3,7 ! O Step 6 cannot be done without DN Frst! 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. ( A ! B ) !⇠ ( C _ D ) ( E $ F ) ! D E ! F F ! E SHOW: ( A ! B ) E $ F D C _ D ⇠⇠ ( C _ D ) ( A ! B ) Pr Pr Pr Pr DD 3,4 $ I 2,6 ! O 7 _ I 8 DN 1,9 ! O E. Conditional Derivation (CD) We have both In and Out rules for all our connectives, except for the arrow. There is no ! I rule! This makes deriving the conclusion of arguments with
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