SOLUTION: 1. (K ¡ L) ⊃ (M ● N) 2. (N ¡ O) ⊃ (P ● ∼K)/ ∼K

Algebra ->  Proofs -> SOLUTION: 1. (K ¡ L) ⊃ (M ● N) 2. (N ¡ O) ⊃ (P ● ∼K)/ ∼K       Log On


   

Question 1208772: 1. (K ¡ L) ⊃ (M ● N) 2. (N ¡ O) ⊃ (P ● ∼K)/ ∼K

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
I will assume " ¡ " means " or" or "disjunction.

1. (K ¡ L) ⊃ (M ● N)  
2. (N ¡ O) ⊃ (P ● ∼K)   / ∼K
                3. ~~K       Assumption for indirect proof
                4. K           3, double negation
                5. K ¡ L       4, addition    
                6. M ● N     1,5, modus ponens
                7. N ● M       6, commutation  
                8. N           7, simplification
                9. N ¡ O       8, addition
               10. P ● ∼K    2,9, modus ponens
               11. ~K ● P     10, commutation
               12. ~K         11, simplification
               13. ~~K ● ~K 3,12, conjunction
14. ~K     Lines 3-13 for indirect proof
 
Edwin