SOLUTION: can i have help with these two proofs? 1. X >Y 2. (Y v ~X) > (Y > Z) / ~Z > ~X

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Question 1010296: can i have help with these two proofs?
1. X >Y
2. (Y v ~X) > (Y > Z) / ~Z > ~X
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
can i have help with these two proofs?
1. X >Y
2. (Y v ~X) > (Y > Z) / ~Z > ~X
The conclusion is equivalent to ~~X > ~~Z by transposition
which is equivalent to X > Y by double negation.
We first form a conditional proof for X > Z:

1. X > Y 
2. (Y v ~X) > (Y > Z)         / X > Z

  |3. X               ACP
  |4. Y            1,3 MP
  |5. Y v ~X         4 Add
  |6. Y > Z        2,5 MP
7. X > Z           3-6, CP
8. ~Z > ~X           7, Transposition
     



 1. (A & U) < > ~R 
 2. ~(~R v ~A)            / ~U

 3. ~~R & ~~A          2, DM
 4. R & A              3, DN
 5. ~~R < > ~(A & U)   1, TR (transposition)
 6. R <> ~(A & U)      5, DN
 7. R                  4, Simp.
 8. ~(A & U)           6,7, MP
 9. ~A v ~U            8, DM
10. A                  4, Simp.
11. ~~A                10, DN
12. ~U                 9,11, DS (disjunctive syllogism)

Edwin
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