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
Naguru
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.
Tim
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.