SOLUTION: Use an ordinary proof (not conditional or indirect) to solve the following arguments 1. P ⊃ ~M 2. C ⊃ M 3. ~L v C 4. (~P ⊃ ~E) • (~E ⊃ ~C) 5. P v ~P /~L

Algebra ->  Proofs -> SOLUTION: Use an ordinary proof (not conditional or indirect) to solve the following arguments 1. P ⊃ ~M 2. C ⊃ M 3. ~L v C 4. (~P ⊃ ~E) • (~E ⊃ ~C) 5. P v ~P /~L      Log On


   

Question 1179971: Use an ordinary proof (not conditional or indirect) to solve the following arguments
1. P ⊃ ~M
2. C ⊃ M
3. ~L v C
4. (~P ⊃ ~E) • (~E ⊃ ~C)
5. P v ~P /~L
Answer by Edwin McCravy(20055) 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. ~P ⊃ ~E                 4, simplification
 7. ~~E ⊃ ~~P               6, transposition
 8. E ⊃ P                   7, double negation
 9. E ⊃ ~M                  8,1 hypothetical syllogism
10. ~E v ~M                 9, material implication
11. ~(E • M)                10, deMorgan's law
12. ~C v M                   2, material implication
13. (~E ⊃ ~C) • (~P ⊃ ~E)   4, commutation
14. ~E ⊃ ~C                 13, simplification
15. ~~E v ~C                14, material implication
16. E v ~C                  15, double negation
17. ~C v E                  16, commutation
18.  (~C v E) • (~C v M)    17,12, conjunction
19. ~C v (E • M)            18, distribution
20. (E • M) v ~C            19, commutation
21. ~C                      20,11, disjunctive syllogism
22. C v ~L                  3, commutation
23. ~L                      22,21 disjunctive syllogism

Edwin