SOLUTION: (P ∨ Q) ⊃ R S ⊃ ~R S ∨ P / Q ⊃ P

Question 1195296: (P ∨ Q) ⊃ R
S ⊃ ~R
S ∨ P / Q ⊃ P

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


 1.  (P ∨ Q) ⊃ R
 2.  S ⊃ ~R
 3.  S ∨ P                / Q ⊃ P

                   | 4. Q          Assumption for Conditional Proof
                   | 5. Q ∨ P      4, Addition
                   | 6. P ∨ Q      5, Commutation
                   | 7. R          6,1 Modus ponens
                   | 8. ~~R ⊃ ~S   2, Transposition
                   | 9. R ⊃ ~S     8, Double negation          
                   |10. ~S         9,7 Modus ponens
                   |11. P          3,10 Disjunctive syllogism
12. Q ⊃ P        lines 4-11        Conditional proof

Edwin

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