1.      ~(U v R)        

2.      (~R v N) ⊃ (P * H)      

3.      Q ⊃ ~H      / ~Q

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1.   ~(U v R)             Premise

2.   (~R v N) ⊃ (P * H)   Premise

3.   Q ⊃ ~H               Premise

4.   ~U * ~R              1, DeMorgan's (DeM)

5.   ~R                   4, Simplification (SIMP) 

6.   ~R v N               5, Addition (ADD)

7.   P * H                6,2  Modus Ponens (MP)

8.   H                    7, SIMP

9.   ~~H                  8, Double Negation (DN)  

10.  ~Q                   9,3  Modus Tollens (MT)



 

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