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1. P -> (Q-> R)
2. ~Q-> ~P
3. ~(S->~P)
4. R

2007-11-10 16:47:51 · 1 answers · asked by chimostrufia_07 1 in Education & Reference Homework Help

1 answers

I'm going to use > for → since it uses fewer keystrokes, and - instead of ~.

1. P > (Q > R)
2. -Q > -P
3. -(S > -P)
4. -R ................. assumption for indirect proof
5. -(-S v -P) ....... 4 material implication
6. S & P ............ 5 DeMorgan
7. P ................... 6 simplification
8. Q > R ............ 1,7 modus ponens
9. Q ................... 2,7 modus tollens
10. R ................. 8,9 mp
11. -R & R ......... 4,10 conjunction
12. R ................. 4-11 indirect proof

2007-11-13 10:54:09 · answer #1 · answered by Philo 7 · 0 0

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