Question 932733: Can someone please help me with this proof using the 18 rules of inference?
> is a horshoe, v is the wedge, * is the dot
1. (S v T) > (S > ~T)
2. (S > ~T) > (T > K)
3. S v T Therefore: S v K
4. S > ~T 1,3 Modus Ponens
5. T > K 2,4 Modus Ponens
6. (S > ~T) * (T > K) 4,5 Conjunction
7. ~T v K 3,6 Constructive Dilemma
8. ~S v ~T 4, Material Implication
9. ~(S*T) 8, DeMorgan's Rule
I have been stuck on this question for hours, and I can't seek to get to S v K.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
1. (S v T) > (S > ~T)
2. (S > ~T) > (T > K)
3. S v T
/ S v K
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4. S > ~T 1,3 Modus Ponens
5. T > K 2,4 Modus Ponens
6. ~~S v T 3 Double Negation
7. ~S > T 6 Material Implication
8. ~S > K 7,5 Hypothetical Syllogism
9. ~~S v K 8 Material Implication
10. S v K 9 Double Negation
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