SOLUTION: 1. ~Fv~G
2. ~F ⊃ Z
3.~G ⊃ ~R
4. (Zv~R) ⊃ (U ⊃ P)
5. ~P. /~U
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Question 1088315: 1. ~Fv~G
2. ~F ⊃ Z
3.~G ⊃ ~R
4. (Zv~R) ⊃ (U ⊃ P)
5. ~P. /~U
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
| Number | Statement | Lines Used | Reason |
|---|
| 1 | ~F v ~G | | |
| 2 | ~F ⊃ Z | | |
| 3 | ~G ⊃ ~R | | |
| 4 | (Z v ~R) ⊃ (U ⊃ P) | | |
| 5 | ~P | | |
| :. | ~U | | |
| 6 | ~~F ⊃ ~G | 1 | Material Implication |
| 7 | F ⊃ ~G | 6 | Double Negation |
| 8 | F ⊃ ~R | 7,3 | Hypothetical Syllogism |
| 9 | ~Z ⊃ ~~F | 2 | Transposition |
| 10 | ~Z ⊃ F | 9 | Double Negation |
| 11 | ~Z ⊃ ~R | 10,8 | Hypothetical Syllogism |
| 12 | ~~Z v ~R | 11 | Material Implication |
| 13 | Z v ~R | 12 | Double Negation |
| 14 | U ⊃ P | 4,13 | Modus Ponens |
| 15 | ~U | 14,5 | Modus Tollens |
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