SOLUTION: Using the logical rules of replacement and implication, I was supposed to solve this logical proof. and am now very lost: (Key: . being used for conjunction + being used for disj

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Question 998980: Using the logical rules of replacement and implication, I was supposed to solve this logical proof. and am now very lost:
(Key: . being used for conjunction
+ being used for disjunction
> being used for implication)
Premise 1: W+P
Premise 2:~(W.S)
Premise 3: ~(S.P)
Conclusion~(S.U)
I have tried everything! Please help.

Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
Premise 1: W+P
Premise 2:~(W.S)
Premise 3: ~(S.P)
                  Conclusion~(S.U) 

4. ~W+~S               Premise 2, DeMorgan's law
5. ~S+~W               4, commutativity
6. ~S+~P               Premise 3, DeMorgan's law 
7. (~S+~W).(~S+~P)     5,6, conjunction 
8. ~S+(~W.~P)          7, distribution
9. ~S+~(W+P)           8, DeMorgan's law (replacement)
10. ~(W+P)+~S          9, commutativity
11. ~~(W+P)            Premise 1, double negation
12. ~S                10,11, disjunctive syllogism   
13. ~S+~U             12, addition
14. ~(S.U)            13, DeMorgan's law

Edwin

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