e can represent by placing a _Grey_ Counter in it.

.-------.
|( )| |
|---|---|
| | |
.-------.

[In the "books" example, this Proposition would be "No old books
are English".]

Similarly we may represent the three similar Propositions "No x are y'",
and "No x' are y", and "No x' are y'".

[The Reader should make out all these for himself. In the
"books" example, these three Propositions would be "No old books
are foreign", &c.]

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.]
pg033
.-------.
|( )| |
|---|---|
| | |
.-------.

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."

Hence these three Propositions are equivalent.

[In the "books" example, these Propositions would be

(1) "No old English books exist;
(2) No old books are English;
(3) No English books are old".]

The two equivalent Propositions, "No x are y" and "No y are x", are said
to be 'Converse' to each other.

[For example, if we were told to convert the Proposition

"No porcupines are talkative",

we should first choose our Univ. (say "animals"), and then
complete the Proposition, by supplying the Substantive "animals"
in the Predicate, so that it would be

"No porcupines are talkative animals", and we should then
convert it, by interchanging its Terms, so that it would be

"No talkative animals are porcupines".]

Similarly we may represent the three similar Trios of equivalent
Propositions; the whole Set of _four_ Trios