SOLUTION: 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

SOLUTION: 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

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
-------------------------------------------------------
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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