Question 1008772: 1. (R v S) > (H & ~G)
2. (K v R) > (G v ~H) / ~R
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Proof by contradiction
| Number | Statement | Lines Used | Reason |
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| 1 | | (R v S) -> (H & ~G) | | | | 2 | | (K v R) -> (G v ~H) | | | | .: | | ~R | | | | 3 | ~~R | | AIP | | 4 | R | 3 | DN | | 5 | R v S | 4 | Add | | 6 | R v K | 4 | Add | | 7 | K v R | 6 | Comm | | 8 | H & ~G | 1,5 | MP | | 9 | ~G & H | 8 | Comm | | 10 | H | 8 | Simp | | 11 | ~G | 9 | Simp | | 12 | G v ~H | 2,7 | MP | | 13 | ~H | 12,11 | DS | | 14 | H & ~H | 10,13 | Conj | | 15 | | ~(~~R) | 3-14 | IP | | 16 | | ~R | 15 | DN |
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Acronyms/Abbreviations Used
Add = Addition
AIP = Assumption for Indirect Proof
Comm = Commutation
Conj = Conjunction
DM = De Morgan's Law
DN = Double Negation
DS = Disjunctive Syllogism
IP = Indirect Proof (aka proof by contradiction)
MP = Modus Ponens
Simp = Simplification
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