Question 607845: This may seem easy, but I don't get how to find the answer to this
1. F <-> G
with the final answer of -F <-> -G
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! If F <--> G, then (F -> G) * (G -> F)
We can then use simplification to get F -> G and G -> F
We can then use transposition to get ~G -> ~F and ~F -> ~G
From there, we can then recombine the two last expressions using the conjunction rule to get (~G -> ~F) * (~F -> ~G)
Finally, you can then use the material equivalence rule to go from (~G -> ~F) * (~F -> ~G) to ~G <--> ~F
Hopefully these steps and ideas make sense. If not, let me know. Thanks.
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