SOLUTION: S>(~UB) / (~H>S)>(~H>B)
Using conditional proof
The horseshoe is >
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Question 1003230: S>(~UB) / (~H>S)>(~H>B)
Using conditional proof
The horseshoe is >
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
| Number | Statement | Lines Used | Reason |
|---|
| 1 | | S > (~U * B) | | |
| .: | | (~H > S) > (~H > B) | | |
| | | 2 | ~H > S | | ACP |
| | | 3 | ~H > (~U * B) | 2,1 | HS |
| | | 4 | ~~H v (~U * B) | 3 | MI |
| | | 5 | H v (~U * B) | 4 | DN |
| | | 6 | (H v ~U) * (H v B) | 5 | Dist |
| | | 7 | (H v B) * (H v ~U) | 6 | Comm |
| | | 8 | H v B | 7 | Simp |
| | | 9 | ~~H v B | 8 | DN |
| | | 10 | ~H > B | 9 | MI |
| 11 | | (~H > S) > (~H > B) | 2-10 | CP |
Acronyms/Abbreviations used:
ACP = Assumption for Conditional Proof
CP = Conditional Proof
HS = Hypothetical Syllogism
MI = Material Implication
DN = Double Negation
Comm = Commutation
Dist = Distribution
Simp = Simplification
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