SOLUTION: What is the ordinary proof to solve the following argument? P ⊃ ~M C ⊃ M ~L v C (~P ⊃ ~E) • (~E ⊃ ~C) P v ~P /~L

Algebra ->  Proofs -> SOLUTION: What is the ordinary proof to solve the following argument? P ⊃ ~M C ⊃ M ~L v C (~P ⊃ ~E) • (~E ⊃ ~C) P v ~P /~L       Log On


   

Question 1157735: What is the ordinary proof to solve the following argument?
P ⊃ ~M
C ⊃ M
~L v C
(~P ⊃ ~E) • (~E ⊃ ~C)
P v ~P /~L
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

 1.  P ⊃ ~M
 2.  C ⊃ M
 3.  ~L v C
 4.  (~P ⊃ ~E) • (~E ⊃ ~C)
 5.  P v ~P                     /~L

 6.  (~E ⊃ ~C) • (~P ⊃ ~E)        4, commutation
 7.  ~E ⊃ ~C                      6, simplification
 8.  ~~C ⊃ ~~E                    7, transposition
 9.  C ⊃ E                        8, double negation
10. ~P ⊃ ~E                       4, simplification
11. ~~E ⊃ ~~P                    10, transposition
12. E ⊃ P                        11, double negation
13. C ⊃ P                        9,12 hypothetical syllogism
14. C ⊃ ~M                       13,1, hypothetical syllogism
15. ~M ⊃ ~C                      2, transposition
16. C ⊃ ~C                       14,15, hypothetical syllogism
17. ~C v ~C                      16, material implication
18. ~C                           17, tautology
19. C v ~L                        3, commutation
20. ~L                           19,18, disjunctive syllogism   

Edwin