There's no gameboard when G is not in 1 because the second rule states that G is in 1. This means always and forever. There is no scenario in which G cannot be in 1.
Also, rule 3 is 1-->/7. The contrapositive is 7-->/1.
Well, not necessarily because there's nothing to say that G had to be in 1 or 7. You would only split the game board up like that if there was only 1 variable that could go in either 1 or 7. In this case, G and N could go in 7, and all three of them could go in 1 (if you removed the G=1 rule).
It depends on how strong your logic skills are and how familiar you are with contrapositives. If you have a really good understanding of them, then writing out the contrapositive for every conditional rule would largely just be symbolism for you. However, if you're still a little shaky then writing out the CP is great practice. Writing out the CP can also be useful for the less than straightforward conditionals as well.
Comments
Also, rule 3 is 1-->/7. The contrapositive is 7-->/1.
If there was no second rule that states G must be in slot 1, then there would have been 2 boards, slot 1 G and slot 7 G, correct?
Question, whenever there is conditional logic in a game, do we contropose like in LR?