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

Question 1066635: 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
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

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

John

My calculator said it, I believe it, that settles it

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SOLUTION: write a direct proof using the eight rules of inference ~M, (~M � ~N) &#8594; (Q &#8594; P), P &#8594; R, ~N, therefore, Q &#8594; R Thank you in advance

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