SOLUTION: I'm having a hard time constructing a proof for the following argument. M&~Q M->S S->P And the goal is ~(P->Q)

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Question 1028017: I'm having a hard time constructing a proof for the following argument.
M&~Q
M->S
S->P
And the goal is ~(P->Q)
Found 2 solutions by richard1234, Edwin McCravy:
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
M is true, so apply rules 2 and 3:

M --> S --> P, so P is true
Q is not true.

Therefore it is not true that P implies Q.

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
 1.  M&~Q
 2.  M->S
 3.  S->P    /~(P->Q)

 4.  M          1, siomplification
 5.  S          2,4, modus ponens
 6.  P          3,5, modus ponens
 7.  ~Q&M       1, commutation
 8.  ~Q         7, simplification
 9.  P&~Q       6,8, conjunction of premises
10.  ~~P&Q      9, double negation
11.  ~(~PvQ)    10, DeMorgan's law
12.  ~(P->Q)    11, Material implication

Edwin