SOLUTION: Use natural deduction to derive the conclusion in each problem. Use an ordinary proof (not conditional or indirect proof): 1.E ⊃ (S ⊃ T) 2.(∼L • M) ⊃ (S • E)

Algebra ->  Proofs -> SOLUTION: Use natural deduction to derive the conclusion in each problem. Use an ordinary proof (not conditional or indirect proof): 1.E ⊃ (S ⊃ T) 2.(∼L • M) ⊃ (S • E)       Log On


   

Question 1207678: Use natural deduction to derive the conclusion in each problem.
Use an ordinary proof (not conditional or indirect proof):

1.E ⊃ (S ⊃ T)
2.(∼L • M) ⊃ (S • E)
3.∼(T ∨ L) / ∼M
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

1.E ⊃ (S ⊃ T)
2.(∼L • M) ⊃ (S • E)
3.∼(T ∨ L) / ∼M

4. ∼T • ~L            3, DeMorgan's law
5. ~T                 4, Simplifiction
6. (E • S) ⊃ T        1, Importation
7. ~(E • S)         6,5, Transposition
8. ~(S • E)           7, Commutation
9.~(~L • M)         2,8, Transposition
10. ~~L ∨ ~M          9, DeMorgan's law
11. L ∨ ~M           10, Double negation
12. ∼L • ~T           4, Commutation
13. ~L               12, Simplification
14. ~M            11,13, Modus tollens                  

I used Importation in step 6.  I assumed you can use things 
like Importation, Exportation, Material implication. Let me
know if you can't.

Edwin