Question 1005236: F > ~G
~F > (H > ~G)
(~I v ~H) > ~~G
~I
/ ~H
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
| Number | Statement | Lines Used | Reason |
|---|
| 1 | F > ~G | | | | 2 | ~F > (H > ~G) | | | | 3 | (~I v ~H) > ~~G | | | | 4 | ~I | | | | :. | ~H | | | | 5 | (~I v ~H) > G | 3 | DN | | 6 | ~(~I v ~H) v G | 5 | MI | | 7 | (~~I * ~~H) v G | 6 | DM | | 8 | (I * H) v G | 7 | DN | | 9 | G v (I * H) | 8 | Comm | | 10 | (G v I) * (G v H) | 9 | Dist | | 11 | G v I | 10 | Simp | | 12 | I v G | 11 | Comm | | 13 | G | 12,4 | DS | | 14 | ~~G | 13 | DN | | 15 | ~F | 1,14 | MT | | 16 | H > ~G | 2,15 | MP | | 17 | ~H | 16,14 | MT |
Abbreviation/Acronyms Used
Comm = Commutation
Dist = Distribution
DM = De Morgan's Law
DN = Double Negation
DS = Disjunctive Syllogism
MI = Material Implication
MP = Modus Ponens
MT = Modus Tollens
Simp = Simplification
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