SOLUTION: 7)I can only use the 8 Rules of Inference. Need help!!! 1. (T → C) → ~F 2. S → C 3. T → S 4. F v ~P /~P ___________ ___________ 5. 6. 7.

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Question 189539: 7)I can only use the 8 Rules of Inference. Need help!!!
1. (T → C) → ~F
2. S → C
3. T → S
4. F v ~P /~P
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Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Here, you'll use a hypothetical syllogism to isolate ~F (using modus ponens) which will then get you ~P (through a disjunctive syllogism). 

1. (T -> C) -> ~F
2. S -> C
3. T -> S
4. F v ~P /~P
----------------------
5.  T -> C            3,2   Hypothetical Syllogism
6.  ~F                1,5   Modus Ponens
7.  ~P                4,6   Disjunctive Syllogism

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