Question 1171292
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1.  O --> (H * M)
2.  (O --> G) --> (H --> ~M)
3.  ~G --> (~H v ~M)                 .·. H --> ~M

4.  ~(~H v ~M) --> ~~G         3, Transposition
5. (~~H * ~~M) --> ~~G         4, DeMorgan's Law
6. (H * M) --> G               5, Double Negation
7. O --> G                     1,6, Hypothetical Syllogism 
8. H --> ~M                    2,7, Modus Ponens

Edwin</pre>