This means "no x are y, AND none are y'," i.e. "no new are nice,
AND none are not-nice": which leads to the rather curious result
that "no new exist," i.e. "no Cakes are new." This is because
"nice" and "not-nice" make what we call an 'EXHAUSTIVE' division
of the class "new Cakes": i.e. between them, they EXHAUST the whole
class, so that all the new Cakes, that exist, must be found in one
or the other of them.

And now suppose you had to represent, with counters the contradictory
to "no Cakes are new", which would be "some Cakes are new", or,
putting letters for words, "some Cakes are x", how would you do
it?

This will puzzle you a little, I expect. Evidently you must put
a red counter SOMEWHERE in the x-half of the cupboard, since you
know there are SOME new Cakes. But you must not put it into the
LEFT-HAND compartment, since you do not know them to be NICE: nor
may you put it into the RIGHT-HAND one, since you do not know them
to be NOT-NICE.

What, then, are you to do? I think the best way out of the
difficulty is to place the red counter ON THE DIVISION-LINE between
the xy-compartment and the xy'-compartment. This I shall represent
(as I always put '1' where you are to put a red counter) by the
diagram


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