SOLUTION: (G • S) → D (S → D) → P G / P

Question 1141206: (G • S) → D
(S → D) → P
G / P
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!

1. (G • S) → D
2. (S → D) → P
3. G                                 /P

                       | 4. ~P         Assumption for indirect proof
                       | 5. ~(S → D)   2,4, Modus tollens
                       | 6. ~(~S v D)  5, Material implication
                       | 7. ~~S • ~D   6, deMorgan's law
                       | 8. S • ~D     7, double negation
                       | 9. ~D • S     8, commutation
                       |10. ~D         9, simplification
                       |11. ~(G • S)   1,10, Modus tollens
                       |12. ~G v ~S    11, deMorgan's law
                       |13. S • ~D     9, commutation
                       |14. S          13, simplification
                       |15. ~S v ~G    12, commutation
                       |16. ~~S        14,  double negation
                       |17. ~G         15,16 disjunctive syllogism
                       |18. G • ~G     2,17 conjunction 
19. P                Lines 4-18 for indirect proof

Edwin

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