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)

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) (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(20055) (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

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