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help with this philosophy stuff!?
Im stuck on these philosophy problems and I just don't know what to do. Any help would be appreciated:
1. Prove the following valid using any of the eight inference rules.
A. (A v B) > O
B. G v ( K v J)
C. K > A
D. J > B
E. ~G / O
2. Prove the following using any of the eight inference rules of Chapters 18 and 19.
A. (A v B) > ~L
B. L v G
C. H > (A v B)
D. O > H
E. E & O / G v Z
2 Answers
- ?Lv 76 years ago
1) Please wait. Have patience. I can help you in this connection in several ways. I have got that potential. In the meantime, please don't jump into any hasty or wrong conclusions about this stuff.
2) I can easily take you out of this serious problem. Unfortunately, I do not know your present exact location. Otherwise in no time, I can lift you through a long rope which I am having in my helicopter. Then we can both go to the Maths professor who is my close friend. He knows every thing that is now hidden in your heart.
Source(s): compiled. - TimLv 66 years ago
1. Show O ............. Proven Directly by 9
2. .. G v (K v J) ...... Prem. B
3. .. ~G ................. Prem. E
4. .. K v J ............... 2, 3, Disj. Elim.
5. .. K → A ........... Prem. C
6. .. J → B ............ Prem. D
7. .. A v B ............. 4, 5, 6, Con. Dil.
8. .. (A v B) → O .... Prem. A
9. .. O .................... 7, 8, MP
1. Show G v Z ......... Proven Indirectly by 13, 14
2. .. ~(G v Z) ........... Assume Neg.
3. .. ~G ^ ~Z ........... 2, DeMorgan's Law
4. .. E ^ O ............... Prem. E
5. .. O ..................... 4, Simp.
6. .. O → H ............. Prem. D
7. .. H ..................... 5, 6, MP
8. .. H → ( A v B) ..... Prem. C
9. .. A v B ................ 7, 8, MP
10.. (A v B) → ~L ..... Prem. A
11.. ~L ..................... 9, 10, MP
12.. L v G ................ Prem. B
13.. G ..................... 11, 12, Disj. Elim.
14.. ~G ................... 3, Simp.