SOLUTION: Super lose on this please help
~(Lv~Z)&B
(O&Z)>L
(~OvR)>~G
/~G
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Question 981173: Super lose on this please help
~(Lv~Z)&B
(O&Z)>L
(~OvR)>~G
/~G
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Abbreviations/Acronyms Used:
Add = Addition
Comm = Commutation
DM = De Morgan's Law
DN = Double Negation
DS = Disjunctive Syllogism
MP = Modus Ponens
MT = Modus Tollens
Simp = Simplification
Number | Statement | Lines Used | Reason |
---|
1 | ~(L v ~Z) & B | | |
2 | (O & Z) > L | | |
3 | (~O v R) > ~G | | |
:. | ~G | | |
4 | ~(L v ~Z) | 1 | Simp |
5 | ~L & ~~Z | 4 | DM |
6 | ~L & Z | 5 | DN |
7 | ~L | 6 | Simp |
8 | ~(O & Z) | 2,7 | MT |
9 | ~O v ~Z | 8 | DM |
10 | Z & ~L | 6 | Comm |
11 | Z | 10 | Simp |
12 | ~~Z | 11 | DN |
13 | ~Z v ~O | 9 | Comm |
14 | ~O | 13,12 | DS |
15 | ~O v R | 14 | Add |
16 | ~G | 3,15 | MP |
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