This tells us that at least one Thing, in the West Half, is also in the North Half. Hence it must be in the space common to them, that is, in the North-West Cell. Hence the North-West Cell is occupied. And this we can represent by placing a Red Counter in it.
[In the “books” example, this Proposition would be “Some English books are old”.]
Similarly we may represent the three similar Propositions “Some y are x′”, “Some y′ are x”, and “Some y′ are x′”.
[The Reader should make out all these for himself. In the “books” example, these three Propositions would be “Some English books are new”, &c.]
We see that this one Diagram has now served to represent no less than three Propositions, viz.
(1) “Some xy exist;
(2) Some x are y;
(3) Some y are x”.
Hence these three Propositions are equivalent.
[In the “books” example, these Propositions would be
(1) “Some old English books exist;
(2) Some old books are English;
(3) Some English books are old”.]