SOLUTION: I need the following proof :) PLEASE. I am struggling... 1. P-> (~Q & R) 2. (Qv~R) ->S 3. ~SvP Conclusion: ~Q THANK YOU!

Algebra ->  Proofs -> SOLUTION: I need the following proof :) PLEASE. I am struggling... 1. P-> (~Q & R) 2. (Qv~R) ->S 3. ~SvP Conclusion: ~Q THANK YOU!       Log On


   

Question 929929: I need the following proof :) PLEASE. I am struggling...
1. P-> (~Q & R)
2. (Qv~R) ->S
3. ~SvP
Conclusion: ~Q
THANK YOU!
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
1. P-> (~Q&R)
2. (Qv~R) ->S
3. ~SvP 
Conclusion: ~Q 

4. (~~Qv~R) -> S   2,DN        (double negation)
5. ~(~Q&R)  -> S   4,DM        (deMorgan's law) 
6. ~S -> ~~(~Q&R)  5,CP        (contrapositive)
7. ~S -> (~Q&R)    6,DN        (double negation) 
8. ~Q&R            7,1,3,CD    (constructive dilemma)
9. ~Q              8,simp.     (simplification of a conjunction)

Edwin