~ is negation
-->is conditional
^ is disjunction
& is conjunction
1. P--> ~M
2. C--> M
3. ~L ^ C
4. (~P-->~E)& (~E-->~C)
5. P^ ~P / ~L
I spent the night but still couldnt prove its validity!!!
PLZ can someone gimme a hand? (Including the rules used if possible?)
THX a lot!!!!
Can anybody help me on this natural deduction proof?
2011-05-02 9:13 am
回答 (1)
2011-05-02 9:32 pm
✔ 最佳答案
1. P > ~M Premise2. C > M Premise
3. ~L v C Premise
4. (~P > ~E) & (~E > ~C) Premise
5. ~~P > ~M 1 Double Negation
6. M > ~P 5 Transposition
7. C > ~P 2,6 Hypothetical Syllogism
8. ~P > ~E 4 Simplification
9. C > ~E 7,8 Hypothetical Syllogism
10. (~E > ~C) & (~P > ~E) 4 Commutation
11. ~E > ~C 10 Simplification
12. C > ~C 9,11 Hypothetical Syllogism
13. ~C v ~C 12 Implication
14. ~C 13 Tautology
15. C v ~L 3 Commutation
16. ~L 14,15 Disjunctive Syllogism
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