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

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) (Show Source): You can put this solution on YOUR website!
One problem at a time
Answer by jim_thompson5910(35256) (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
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SOLUTION: Use an ordinary proof to solve 1) 1.E &#8835; (S &#8835; T) 2.(~L &#8901; M)&#8835;(S &#8901; E) 3.~ (T v L) /~M

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