Bi-conditionals vs Not both - Please help

changba94

I just wanted to clarify when to use not both (F---->/C) vs a bi-conditional (F/C). My current understanding is that if the in/out game has only two categories, I should use the bi-conditional representation because it represents the only possibilities because the two variables, in this case "F&C", cannot be in or out together. Whereas I should use the not both representation when there are more more than two groups because while the variables do not have to be together, there are other categories that they will be able to go in.