SOLUTION: 1. P ⊃ [ ( L v M ) ⊃ ( N • O ) ] 2. ( O v T ) ⊃ W / P ⊃ ( M ⊃ W )

Question 1188400: 1. P ⊃ [ ( L v M ) ⊃ ( N • O ) ]
2. ( O v T ) ⊃ W / P ⊃ ( M ⊃ W )

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


Don't skip a space just after "(" or "[" and don't skip a space 
just before  ")" or "]".  It looks confusing when you do. 

Since by exportation the conclusion P ⊃ (M ⊃ W) is 
equivalent to (P • M) ⊃ W, we will assume P • M for 
a conditional proof

1. P ⊃ [(L v M) ⊃ (N • O)]
2. (O v T) ⊃ W                              / P ⊃ (M ⊃ W), same as (P • M) ⊃ W
 


 
                      |3. P • M                   ACP
                      |4. P                   3, Simplification
                      |5. (L v M) ⊃ (N • O)   1,4, Modus ponens
                      |6. M • P               3, Commutation
                      |7. M                   6, Simplification
                      |8. M v L               7, Addition
                      |9. L v M               8, Commutation           
                     |10. N • O               5,9 Modus ponens
                     |11. O • N               10, Commutation
                     |12. O                   11, Simplification
                     |13. O v T               12, Addition
                     |14. W                   2,13, Modus ponens
15. (P • M) ⊃ W         lines 3-14         Conditional proof.
16. P ⊃ (M ⊃ W)                            15, Exportation   

Edwin

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