SOLUTION: write a direct proof using the eight rules of inference ~M, (~M • ~N) → (Q → P), P → R, ~N, therefore, Q → R Thank you in advance

1.  ~M
2.  (~M & ~N) -> (Q -> P)
3.  P -> R
4.  ~N                :.  Q -> R

5.  ~M & ~N               1, 4 Conjunction Introduction
6.  Q -> P                5, 2 Modus Ponens
7.  (Q -> P) & (P -> R)   3, 6 Conjuction Introduction
8.  :. Q -> R             7    Hypothetical Syllogism