Hello, I need help writing proofs for a logic and moral reasoning philosophy class. The proofs are for: 1. Premises: q -> (q &~ q) Conclusion: ~q 2. Premises: k & l
HW 9
Write proofs for the following problems.
(1)
Premises:
g -> (~o -> (g -> d))
o V g
~o
Conclusion:
| |
| |
| |
| | DS 2, 3 |
| MP 1, 4 |
| 6. g -> d | MP 5, 3 |
| 7. d | MP 6, 4 |
(2)
Premises:
(u & (~(~p))) -> q
~o -> u
~p -> o
~o & t
Conclusion:
q
| 1. (u & (~(~p))) -> q | A |
| 2. ~o -> u | A |
| 3. ~p -> o | A |
| 4. ~o & t | A |
| 5. ~o | Simp 4 |
| 6. u | MP 2, 5 |
| 7. ~~p | MT 3, 5 |
| 8. u & ~~p | Conj 6, 7 |
| 9. q | MP 1, 8 |
(3)
Premises:
m -> (u -> h)
(h V ~u) -> f
Conclusion:
m -> f
| 1. m -> (h V ~u) | |
| 2. (h V ~u) -> f | |
| --3. m | CA |
| --4. u -> h | MP 1, 3 |
| --5. ~u V h | MI 4 |
| --6. h V ~u | Commut 5 |
| --7. f | MP 2, 6 |
| 8. m -> f | CP 3-7 |
(4)
Premises:
(i -> e) -> c
c -> ~c
Conclusion:
| 1. (i -> e) -> c | A |
| 2. c -> ~c | |
| 3. ~c V ~c | MI 2 |
| 4. ~c | Taut 3 |
| 5. ~(i -> e) | MT 1, 4 |
| 6. ~(~i V e) | MI 5 |
| 7. ~~i & ~e | DM |
| 8. ~~i | Simp 7 |
| 9. i | DN 8 |
(5)
Premises:
i -> ~(g V f)
~t V i
Conclusion:
~f
| 1. i -> ~(g V f) | |
| 2. ~t V i | |
| 3. t | |
| 4. ~~t | DN 3 |
| 5. i | DS 2, 4 |
| 6. ~(g V f) | MP 1, 5 |
| 7. ~g & ~f | DM 6 |
| 8. ~f | Simp 7 |
