SOLUTION: ~M, (~M • ~N) → (Q → P), P → R, ~N, therefore, Q → R

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Question 1089635: ~M, (~M • ~N) → (Q → P), P → R, ~N, therefore, Q → R
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
                                          
1.  ~M                            Premise
2. (~M• ~N)→ (Q → P)              Premise  
3.  P → R                         Premise
4.  ~N                            Premise
    {  To show conclusion:  Q → R  }
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5.  ~M• ~N                        1,4  Conjunction (Conj)                   
6.  Q → P                         5,2  Modus Ponens (MP)
::7.   Q                                  Assumption (begin conditional proof, CP)
::8.   P                                  7,6 MP
::9.   R                                  8,3 MP
10.   Q → R                       7,8,9 End of CP,  and the conclusion

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Steps 7-9 are conditional. Essentially they show that if Q is true then the logical path through the premises is that R follows, hence Q—>R.
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Warning: I am a bit rusty with these proofs, so a 2nd opinion won't hurt.