SOLUTION: Use an ordinary proof to solve 1) 1.E ⊃ (S ⊃ T) 2.(~L ⋅ M)⊃(S ⋅ E) 3.~ (T v L) /~M

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Question 293877: Use an ordinary proof to solve
1) 1.E ⊃ (S ⊃ T)
2.(~L ⋅ M)⊃(S ⋅ E)
3.~ (T v L) /~M
Found 2 solutions by richwmiller, jim_thompson5910:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
One problem at a time

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) 
Therefore, ~M
-------------------------------------------------------
4.  (E & S) -> T                         1         Exp
5.  (~L & M) -> T                        2,4       HS
6.  ~T & ~L                              3         DM
7.  ~L & ~T                              6         Comm
8.  ~T                                   6         Simp
9.  ~L                                   7         Simp
10. ~(~L & M)                            5,8       MT
11. ~~L v ~M                             10        DM
12. ~M                                   11,9      DS



Abbreviations/Acronyms Used:

Comm = Commutation
DM = De Morgan's Law
DS = Disjunctive Syllogism
Exp = Exportation
HS = Hypothetical Syllogism
MT = Modus Tollens
Simp = Simplification