SOLUTION: Use indirect proof: 1. (P ∨ F) ⊃ (A ∨ D) 2. A ⊃ (M • ∼P) 3. D ⊃ (C • ∼P) / ∼P

Question 1188427: Use indirect proof:
1. (P ∨ F) ⊃ (A ∨ D)
2. A ⊃ (M • ∼P)
3. D ⊃ (C • ∼P) / ∼P

Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!

1. (P ∨ F) ⊃ (A ∨ D)
2. A ⊃ (M • ∼P)
3. D ⊃ (C • ∼P) / ∼P

               4.|~~P                   AIP
               5.|P                  4, Double negation 
               6.|P∨F                5, Addition
               7.|A∨D              1,6, Modus Ponens 
               8.|(M•∼P)∨(C•∼P)  2,3,7, Constructive Dilemma
               9.|(∼P•M)∨(~P•C)      8, Commutation 
              10.|∼P•(M∨C)           9, Distribution
              11.|~P                10, Simplification  
              12.|P•~P            5,11, Conjunction
13. ~(~~P)                        4-12, Indirect Proof 
14. ~P                              13, Double Negation

Edwin

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