Pythagoras: You have to be kidding me? Math?

I have a math degree as it turns out, but this is a question of the english language.

If you have borne of many checkers it is also true that you have borne off a checker. If I ask "Has player x has borne off a checker?" the answer to that question doesn't switch to being "No" just because I bear off a second!!!

If you want to ask about one checker you have to use the word "one". i.e. "Have you borne off one checker?". This is probably ambiguous enough to warrant the word exactly being inserted.

The use of "Else" is simple to understand and needn't be complicated by the use of set theory in my opinion. In this case there is no intersection of sets, you can't be gammoned and backgammoned at the same time.