SOLUTION: Select the conclusion that follows in a single step from the given premises. 1. ~(G • H) 2. ~F > H 3. (G > ~F) • (~F > G)

Algebra ->  Proofs -> SOLUTION: Select the conclusion that follows in a single step from the given premises. 1. ~(G • H) 2. ~F > H 3. (G > ~F) • (~F > G)       Log On


   

Question 1180012: Select the conclusion that follows in a single step from the given premises.
1. ~(G • H)
2. ~F > H
3. (G > ~F) • (~F > G)
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
 1. ~(G • H)
 2. ~F > H
 3. (G > ~F) • (~F > G)

 4. (~F > G) • (G > ~F)      3, commutation 
 5. ~F > G                   4, simplification
 6, ~F > (G • H)             5,2, composition
 7. ~~F                      6,1, modus tollens  
 8. F                        7, double negation
 9. G > ~F                   3, simplification
10. ~G                       9,7 modus tollens
11. F • ~G                   8,10 conjunction

You did not list the choices, but most likely, 
the conclusion is step 11, which is

F • ~G

Edwin