SOLUTION: Construct a regular proof to derive the conclusion of the following argument: 1. X >Y 2. (Y v ~X) > (Y > Z) / ~Z > ~X I have attempted to use Addition to get X > (Y V

Algebra ->  Proofs -> SOLUTION: Construct a regular proof to derive the conclusion of the following argument: 1. X >Y 2. (Y v ~X) > (Y > Z) / ~Z > ~X I have attempted to use Addition to get X > (Y V      Log On


   

Question 1116996: Construct a regular proof to derive the conclusion of the following argument:
1. X >Y
2. (Y v ~X) > (Y > Z) / ~Z > ~X
I have attempted to use Addition to get X > (Y V ~X) from line 1 and no proof checkers that I have attempted will accept it.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
I think ADD will be too simple to make the proof work. Certainly more steps will be required after you use ADD. The proof below works (there may be other non-conditional proofs as well): 
1.  X—>Y                   Premise
2.  (Y v ~X) —>  (Y—>Z)    Premise
3.  Y v ~X                 1, Material Implication (MI)  [ (A—>B)   <—>  (~A v B)  and  (~A v B ) <—> (B v ~A)  ]
4.  Y—>Z                   3,2  Modus Ponens (MP)
5. ::  ~Z                  Condition Proof (CP) assumption
6. ::  ~Y                  5,4  Modus Tollens (MT)
7. ::  ~X                  6,3  Disjunctive Syllogism (DS)
8. ~Z —> ~X                5,7  CP  (done)