SOLUTION: Could you please help me solve the following proof? I have worked a few lines after the conclusion but am stuck after that. 1. E>(S>T) 2. (~L*M) > (S*E) 3. ~(TvL) // ~

Algebra ->  Proofs -> SOLUTION: Could you please help me solve the following proof? I have worked a few lines after the conclusion but am stuck after that. 1. E>(S>T) 2. (~L*M) > (S*E) 3. ~(TvL) // ~      Log On


   

Question 607200: Could you please help me solve the following proof? I have worked a few lines after the conclusion but am stuck after that.
1. E>(S>T)
2. (~L*M) > (S*E)
3. ~(TvL) // ~M
4. (E*S) >T 1. Exportation
5. ~T*~L 3. DeMorgans
6. ~T 5. Simplification
7. ~(E*S) 4,6 Modus Tollens
Key: > equals wedge
* equals dot
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1.  E > (S > T)
2.  (~L * M) > (S * E)
3.  ~(T v L)                    // ~M
-------------------------------------------------------
4.   (E * S) >T
5.   ~T * ~L
6.   ~T
7.   ~(E * S)
8.   ~(S * E)                    7       Commutation
9.   ~(~L * M)                   2,8     Modus Tollens
10.  ~~L v ~M                    9       De Morgan's Law
11.  L v ~M                      10      Double Negation
12.  ~L * ~T                     5       Commutation
13.  ~L                          12      Simplification
14.  ~M                          11,13   Disjunctive Syllogism