1. PvR                  Premise

2. ~Pv(Q.R)          Premise

3. R→Q.S            Premise
…………..

 

Q.S

 

Proof

 

4. (~PvQ).(~PvR)        2 DMorgan

5. ~PvR                        4. Simplification

6. (P. ~P)vR               1,5  Conjunction

7. R                              6 Simplification

8. Q.S                        3,7 Modus Ponen

 

 

                                                                      ****