SOLUTION: Hi! I really could use some help solving these two proofs below. I also included instructions!
Instructions: You must construct a proof for two of the following. All proofs inc
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Question 1029291: Hi! I really could use some help solving these two proofs below. I also included instructions!
Instructions: You must construct a proof for two of the following. All proofs include at least 4 steps (besides the original premises).
I have left the section and problem numbers so that you can check your answers online before posting them. Here is the website for checking your answers:
http://www.poweroflogic.com/cgi/menu.cgi
You can expand the readable area to show the whole argument by clicking and dragging on the triangle shape at the bottom right of this area.
Questions from The Power of Logic 5th Edition/Chapter 8/Section 8.3/Part C
15. (~D v E) • (~D v ~F), (E • ~F) → ~G, ~D → ~G ∴ ~G
24. ~O ∴ ~Q → ~(O • P)
Please & Thank you :)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Problem #15
| Number | Statement | Lines Used | Reason |
|---|
| 1 | (~D v E) & (~D v ~F) | | |
| 2 | (E & ~F) -> ~G | | |
| 3 | ~D -> ~G | | |
| :. | ~G | | |
| 4 | ~D v E | 1 | Simp |
| 5 | ~D v ~F | 1 | Simp |
| 6 | D -> E | 4 | MI |
| 7 | D -> ~F | 5 | MI |
| 8 | E -> (~F -> ~G) | 2 | Exp |
| 9 | D -> (~F -> ~G) | 6,8 | HS |
| 10 | (D & ~F) -> ~G | 9 | Exp |
| 11 | (~F & D) -> ~G | 10 | Comm |
| 12 | ~F -> (D -> ~G) | 11 | Exp |
| 13 | D - > (D -> ~G) | 7,12 | HS |
| 14 | (D & D) -> ~G | 13 | Exp |
| 15 | D -> ~G | 14 | Taut |
| 16 | G -> D | 3 | Trans |
| 17 | G -> ~G | 16,15 | HS |
| 18 | ~G v ~G | 17 | MI |
| 19 | ~G | 18 | Taut |
Abbreviations Used:
Comm: Commutation
Exp: Exportation
HS: Hypothetical Syllogism
MI: Material Implication
Simp: Simplification
Taut: Tautology
Trans: Transposition
------------------------------------------------------------------------------------------------------------------------
Problem #24
| Number | Statement | Lines Used | Reason |
|---|
| 1 | ~O | | |
| :. | ~Q -> ~(O & P) | | |
| 2 | ~O v Q | 1 | Add |
| 3 | Q v ~O | 2 | Comm |
| 4 | (Q v ~O) v ~P | 3 | Add |
| 5 | ~(~Q & O) v ~P | 4 | DM |
| 6 | (~Q & O) -> ~P | 5 | MI |
| 7 | ~Q -> (O -> ~P) | 6 | Exp |
| 8 | ~Q -> (~O v ~P) | 7 | MI |
| 9 | ~Q -> ~(O & P) | 8 | DM |
Abbreviations Used:
Add: Addition
Comm: Commutation
DM: De Morgan's Law
Exp: Exportation
MI: Material Implication
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