SOLUTION: I need help finishing this proof. 1. ~ (A v B) 2. E > B 3. E v (G > U) 4. H v (W & X) 5. (H v X) > (U > O) / G > O

Algebra ->  Proofs -> SOLUTION: I need help finishing this proof. 1. ~ (A v B) 2. E > B 3. E v (G > U) 4. H v (W & X) 5. (H v X) > (U > O) / G > O      Log On


   

Question 205446: I need help finishing this proof.
1. ~ (A v B)
2. E > B
3. E v (G > U)
4. H v (W & X)
5. (H v X) > (U > O) / G > O
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1.  ~ (A v B)
2.  E -> B
3.  E v (G -> U)
4.  H v (W & X)
5.  (H v X) -> (U -> O)    / G -> O
-------------------------------------
6.  (H v W) & (H v X)                4      Distribution
7.  (H v X) & (H v W)                6      Commutation
8.  H v X                            7      Simplification
9.  U -> O                         5,8      Modus Ponens
10. ~A & ~B                          1      De Morgan's Law
11. ~B & ~A                         10      Commutation
12. ~B                              11      Simplification
13. ~E                            2,12      Modus Tollens
14. G -> U                        3,13      Disjunctive Syllogism
15. G -> O                        14,9      Hypothetical Syllogism