SOLUTION: I need help deriving the conclusion using the 18 rules of inference. 1. C>(Dv~E) 2. E>(D>F) /C>(E>F)

Question 924847: I need help deriving the conclusion using the 18 rules of inference.
1. C>(Dv~E)
2. E>(D>F) /C>(E>F)

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

1.  C -> (D v ~E)
2.  E -> (D -> F)
/   C -> (E -> F)
----------------------------------------------------------------------
3.  C -> (~E v D)                  1           Commutation
4.  C -> (E -> D)                  3           Material Implication
5.  (C * E) -> D                   4           Exportation
6.  (E * D) -> F                   2           Exportation
7.  (D * E) -> F                   6           Commutation
8.  D -> (E -> F)                  7           Exportation
9.  (C * E) -> (E -> F)            5,8         Hypothetical Syllogism
10. [(C * E) * E] -> F             9           Exportation
11. [C * (E * E)] -> F             10          Association
12. (C * E) -> F                   11          Tautology
13. C -> (E -> F)                  12          Exportation

==============================================================================================================

Let me know if that helps or not. Thanks.

If you need more help, feel free to email me at jim_thompson5910@hotmail.com

My Website: http://www.freewebs.com/jimthompson5910/home.html

RELATED QUESTIONS
Construct proofs using the Rules of Inference and the Rules of Replacement. The... (answered by jim_thompson5910)

I need help deriving the conclusion (using CONDITIONAL proof). You can use all 18 rules. (answered by jim_thompson5910)

can you help me solve this proof using the first 13 rules of inference please?... (answered by jim_thompson5910)

1. A > [B>(C*~D)] 2. (BvE)>(DvE) Therefore, 3. (A*B) > (C*E) Using conditional... (answered by jim_thompson5910)

Please help me create this proof using the 18 rules of inference. I have been working on... (answered by jim_thompson5910)

1. T ⊃ (Q & F) 2. T & C/Q v O I am trying to solve this equation using the... (answered by math_tutor2020)

use the inference rules, replacement rules, indirect proof and/or conditional proof to... (answered by mccravyedwin,Edwin McCravy)

5) I can only use the 8 rules of inference. 1. C → (T → L) 2. ~L 3. ~E... (answered by jim_thompson5910)

Hello, I need help with these proofs. I believe they are propositional logic and require... (answered by jim_thompson5910)