Question 1141257: (D • E) ∨ F, F → C, (D • E) → ∼B, (∼B ∨ C) → (A → P), ∼P ∴ ∼A
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website! 1. (D • E) ∨ F
2. F → C
3. (D • E) → ∼B
4. (∼B ∨ C) → (A → P)
5. ∼P ∴ ∼A
6. [(~B ∨ C) • A] → P 4, Importation
7. ~[(~B ∨ C) • A] 6,5, Modus Tollens
8. ~(~B ∨ C) ∨ ~A 7, deMorgan's law
9. (~~B • ~C) ∨ ~A 8, deMorgan's law
10. (B • ~C) ∨ ~A 9, Double negation
11. ~A ∨ (B • ~C) 10, commutation
12. |~~A Assumption for Indirect Proof
13. |B • ~C 11,12, Disjunctive syllogism
14 |B 13, Simplification
15. |~C • B 13, Commutation
16. |~C 15, Simplification
17. |~F 2,16 Modus Tollens
18. |F ∨ (D • E) 1, Commutation
19. |D • E 18,17, Disjunctive syllogism
20. |~B 3,19 Modus ponens
21. |B • ~B 14,20 Conjunction
22. ~A lines 12-21 indirect proof
Edwin
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