SOLUTION: Prove this with steps please 1 [(A v ~B) v T]->(X->M) 2 (A v R)->(Z->O) 3 A&(X v Z) 4 (M v O)->(A->E) 5 ~E&S //∴H=K

Algebra ->  Proofs -> SOLUTION: Prove this with steps please 1 [(A v ~B) v T]->(X->M) 2 (A v R)->(Z->O) 3 A&(X v Z) 4 (M v O)->(A->E) 5 ~E&S //∴H=K       Log On


   

Question 1204059: Prove this with steps please
1 [(A v ~B) v T]->(X->M)
2 (A v R)->(Z->O)
3 A&(X v Z)
4 (M v O)->(A->E)
5 ~E&S
//∴H=K
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
1 [(A v ~B) v T]->(X->M)
2 (A v R)->(Z->O)
3 A&(X v Z)
4 (M v O)->(A->E)
5 ~E&S
//∴H=K

 6. A                       3, simplification
 7. ~E                      5, simplification
 8. A & ~E                6,7, conjunction 
 9. ~~A & ~E                8, double negation
10. ~(~A v E)               9, DeMorgan's law
11. ~(A-> E)               10, Material implication
12. ~(M v O)             11,4, Transposition
13. ~M & ~O                12, DeMorgan's law  
14. A v ~B                  6, addition
15. (A v ~B) v T           14, addition
16. X -> M               15,1, modus ponens
17. ~M                     13, simplification
18. ~X                  17,16, transposition
19. (X v Z)&A               3, commutation
20. X v Z                  19, simplification
21. Z                   20,18, disjunctive syllogism  
22. A v R                   6, addition
23. Z-> O                   2, modus ponens
24. O                   23,21, modus ponens
25. ~O & ~M                13, commutation
26. ~O                     25, simplification
27. O v (H=K)              24, addition
29. H=K                 27,26, disjunctive syllogism 

Edwin