4. [30pts] A freshmen at University of Oxford, Godel was murdered under mysterious circumstances on Friday evening at a party. Sherlock Holmes is investigating the case and determines the following facts. List of Statement Variables: N = Newton killed Godel H = Hilbert killed Godel W = Weyl killed Godel P = Godel attended the party Np = Newton has Weyl's pocket watch S = Godel stole Weyl's pocket watch. F = Newton tries to frame Weyl (a) Godel's only classmates without alibis are Weyl, Hilbert, and Newton. (b) Godel attending the party on Friday night is sufficient evidence that Hilbert or Newton killed him. (c) Godel stealing Weyl's pocket watch is a necessary condition for Weyl killing Godel. (d) Emmy Noether spotted Godel at the party on Friday night and she saw Newton with Weyl's pocket watch. (e) If Newton has Weyl's pocket watch, then Godel stole it from Weyl (and gave it to Newton). (f) Hilbert was talking all of Friday evening with his alibi Gauss