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