SOLUTION: 1.S>(R&~T) 2.(S&R)>(TvE) 3.(Qv~T)>~E /~S

Question 1198251: 1.S>(R&~T)
2.(S&R)>(TvE)
3.(Qv~T)>~E /~S
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!

1.S>(R&~T)
2.(S&R)>(TvE)
3.(Qv~T)>~E      /~S

              |4.  ~~S       Assumption for indirect proof
              |5.  S         4, double negation
              |6.  R&~T      1,5, modus ponens
              |7.  R         6, simplification
              |8.  ~T&R      6, commutativity
              |9.  ~T        8, simplification
              |10.  S&R      5,6, conjunction
              |11.  TvE      2,10, modus ponens   
              |12.  E        11,9, disjunctive syllogism
              |13.  ~~E      12, double negation
              |14.  ~(Qv~T)  3,13 modus tollens 
              |15.  ~Q&~~T   14, deMorgan's law
              |16.  ~Q&T     15, double negation
              |17.  T&~Q     16, commutation
              |18.  T        17, simplification
              |19.  T&~T     18,9, conjunction
20.  ~S       lines 4-19  indirect proof

Edwin

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