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

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) (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

RELATED QUESTIONS
I. Use an ordinary proof (not conditional or indirect) to solve the following arguments. (answered by CPhill)

Use an ordinary proof (not conditional or indirect) to solve the following arguments. (answered by Edwin McCravy)

Use an ordinary proof (not conditional or indirect) to solve the following arguments. (answered by RBryant)

Use an ordinary proof (not conditional or indirect) to solve the following arguments... (answered by RBryant,Edwin McCravy,math_tutor2020)

I.Use an ordinary proof (not conditional or indirect) to solve the following arguments.... (answered by Edwin McCravy)

III. Use Indirect Proof to solve the following arguments (K v L) ⊃ (M • N) (N v... (answered by jim_thompson5910)

Complete the following proofs using the Conditional Proof method. 1) 1. ~(P ∙... (answered by solver91311)

Use natural deduction to derive the conclusion of the following arguments. Do not use... (answered by math_helper)

Use natural deduction to derive the conclusion in each problem. Use an ordinary... (answered by Edwin McCravy)