8.6 Exercises

A. Complete the following proofs. Each will require an indirect derivation. The last two are challenging.

1. Premises:  (P→R), (Q→R), (PvQ). Conclusion:  R.
   
2. Premises:  ((PvQ)→R), ~R.  Conclusion: ~P.
   
3. Premise:  (~P&~Q).  Conclusion:  ~(PvQ).
   
   Note: This is half of DeMorgan’s law.
4. Premise:  (P→R), (Q→S), ~(R&S). Conclusion:  ~(P&Q).
   
5. Premise:  ~R, ((P→R) v (Q→R)).  Conclusion: (~Pv~Q).
   
6. Premise:  ~R, ((P→R) v (Q→R)).  Conclusion: (~Pv~Q).
   
7. Premise: ~(R v S), (P→R), (Q→S). Conclusion: ~(P v Q).