Let us take, next, the Proposition “No y are x”.
This tells us that no Thing, in the West Half, is also in the North Half. Hence there is nothing in the space common to them, that is, in the North-West Cell. That is, the North-West Cell is empty. And this we can represent by placing a Grey Counter in it.
[In the “books” example, this Proposition would be “No English books are old”.]
Similarly we may represent the three similar Propositions “No y are x′”, “No y′ are x”, and “No y′ are x′”.
[The Reader should make out all these for himself. In the “books” example, these three Propositions would be “No English books are new”, &c.]
We see that this one Diagram has now served to present no less than three Propositions, viz.
(1) “No xy exist;
(2) No x are y;
(3) No y are x.”