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

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Question 1179871: 1. P (horseshoe) ~M
2. C (horseshoe) M
3. ~L v C
4. (~P (horseshoe) ~E) • (~E (horseshoe) ~C)
5. P v ~P /~L

Answer by RBryant(14) (Show Source):
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1. P ⊃ ~M 2. C ⊃ M 3. ~L v C 4. (~P ⊃ ~E) • (~E ⊃ ~C) 5. P v ~P / ∴ ~L --------------------------------------------- 6. ~M ⊃ ~C 2 Transposition 7. P ⊃ ~C 1,6 Hypothetical Syllogism 8. ~P ⊃ ~E 4 Simplification 9. E ⊃ P 8 Transposition 10. (~E ⊃ ~C)• (~P ⊃ ~E) 4 Commutation 11. ~E ⊃ ~C 10 Simplification 12. C ⊃ E 11 Transposition 13. C ⊃ P 9,12 Hypothetical Syllogism 14. C ⊃ ~C 7,13 Hypothetical Syllogism 15. ~C v ~C 14 Material Implication 16. ~C 15 Tautology 17. ~L 3,8 Disjunctive Syllogism QED