SOLUTION: (D • E) ∨ F, F → C, (D • E) → ∼B, (∼B ∨ C) → (A → P), ∼P ∴ ∼A

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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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