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
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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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