SOLUTION: I am trying to work on the following proof. I know I used DEM incorrectly on line 3. I cannot figure out what other rule to use. I tried contraposition, but it does not allow me to

Question 588387: I am trying to work on the following proof. I know I used DEM incorrectly on line 3. I cannot figure out what other rule to use. I tried contraposition, but it does not allow me to break down the lines. I cannot use MT or MP without having x or y by itself. I do not know what other conditional rule to use.
1. X > Y / X . Z > Y
2. ~X v Y CE 1
3. ~X . ~Y DEM 3
4. ~X Simp 3
5. ~Y Simp 3
6. X DS 2,5
7. Y DS 2,4
8 X v Z Add 6
9. Z DS 4,8
10. ~X v Z Conj 4,9
11. X > Z CE 10
12. ~Z > ~X Contrap 11
13. ~Z MT 4,12
14. ~Z v Y Add 13
15. Z > Y CE 14
16. X . Z > Y Conj 6,15
thank you!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Unfortunately you also made a mistake in line 16. Here's one way to derive the conclusion.

1.  X > Y             / (X . Z) > Y
-------------------------
2.  ~X v Y                  1       Material Implication
3.  (~X v Y) v ~Z           2       Addition
4.  ~X v (Y v ~Z)           3       Association
5.  ~X v (~Z v Y)           4       Commutation
6.  (~X v ~Z) v Y           5       Association
7.  ~(X . Z) v Y            6       De Morgan's Law
8.  (X . Z) > Y             7       Material Implication

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