SOLUTION: 3) I can only use the 8 rules of inference... 1. (M v N) → ~S 2. T → (M v N) 3. ~S → ~(M v N) / T → ~(M v N) ___________ ___________ 4. 5. 6.

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Question 189540: 3) I can only use the 8 rules of inference...
1. (M v N) → ~S
2. T → (M v N)
3. ~S → ~(M v N) / T → ~(M v N)
________________________
4.
5.
6.
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
In this proof, all we've used is a hypothetical syllogism. This is like saying "if it rains, then it gets wet outside. If it gets wet outside, then the roads will be slippery. Therefore, if it rains, the roads will be slippery.". Symbolically, this means that


p -> q
q -> r
therefore: p -> r



You'll find that you'll use this rule quite often. 

1. (M v N) -> ~S
2. T -> (M v N)
3. ~S -> ~(M v N) / T -> ~(M v N) 
-------------------------------------
4.  (M v N) -> ~(M v N)              1,3  Hypothetical Syllogism 
5.  T -> ~(M v N)                    2,4  Hypothetical Syllogism

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