You need to do a conditional proof. The first step is to note that you can deduce V from V & ~K by simplification. Then by Addition (or Disjunction Introduction if you prefer), you can deduce V v N. Then by Modus Ponens we conclude F -> ~G.
Now the conditional part. Assume G. Then by Modus Tollens you have ~F. ~F and ~H v F gives us ~H. Then by Modus Ponens, ~H -> I gives us I, then by Modus Ponens again, I -> A gives us A. In summary, assuming G we get A and from A we can conclude A v ~G by Addition.
The alternative is ~G, from which we can conclude A v ~G by addition.
Either way, A v ~G.
John
My calculator said it, I believe it, that settles it
