SOLUTION: 1. G⊃(H⊃K) 2. (H∨∼M)⊃∼K 3. H / ∼G

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Question 1199146: 1. G⊃(H⊃K)
2. (H∨∼M)⊃∼K
3. H / ∼G
Found 2 solutions by math_helper, RBryant:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!


Using -> instead of ⊃



1. G->(H->K)       Premise

2. (Hv~M)-> ~K     Premise

3. H               Premise

// show ~G

4. Hv~M            3, Addition (ADD)

5. ~K              4,2 Modus Ponens (MP)

6. H & ~K          3,5 Conjunction (CONJ)

7. ~(~H v K)       6 DeMorgan's  (DeM)

8. ~(H->K)         7 Material Implication (MI)

9. ~G              8,1 Modus Tollens (MT)

** done **

Answer by RBryant(14) About Me  (Show Source):
You can put this solution on YOUR website!


1. G⊃(H⊃K)
2. (H∨∼M)⊃∼K
3. H                / ∴ ∼G
------------------------------------------------------
4. H v ~M           3,  Add
5. ~K              2,4  M.P.
6. H • ~K          3,5  Conj
7. ~ ~H • ~K        6   D.N. 
8. ~ (~H v K)       7   DeM
9. ~ (H ⊃ K)        8   Impl
10. ~G             1,9   M.T.
                               QED