Similarly for the seven similar Pairs, in terms of x and m, or of y and m.

[pg045]Let us take, next, the Proposition “All x are m.”

We know (see [p. 18]) that this is a Double Proposition, and equivalent to the two Propositions “Some x are m” and “No x are m′ ”, each of which we already know how to represent.

Similarly for the fifteen similar Propositions, in terms of x and m, or of y and m.

These thirty-two Propositions of Relation are the only ones that we shall have to represent on this Diagram.

The Reader should now get his genial friend to question him on the following four Tables.

The Victim should have nothing before him but a blank Triliteral Diagram, a Red Counter, and 2 Grey ones, with which he is to represent the various Propositions named by the Inquisitor, e.g. “No y′ are m”, “Some xm′ exist”, &c., &c.

[pg046]TABLE V.
Some xm exist
= Some x are m
= Some m are x
No xm exist
= No x are m
= No m are x
Some xm′ exist
= Some x are m′
= Some m′ are x
No xm′ exist
= No x are m′
= No m′ are x
Some x′m exist
= Some x′ are m
= Some m are x′
No x′m exist
= No x′ are m
= No m are x′
Some x′m′ exist
= Some x′ are m′
= Some m′ are x′
No x′m′ exist
= No x′ are m′
= No m′ are x′

[pg047]TABLE VI.
Some ym exist
= Some y are m
= Some m are y
No ym exist
= No y are m
= No m are y
Some ym′ exist
= Some y are m′
= Some m′ are y
No ym′ exist
= No y are m′
= No m′ are y
Some y′m exist
= Some y′ are m
= Some m are y′
No y′m exist
= No y′ are m
= No m are y′
Some y′m′ exist
= Some y′ are m′
= Some m′ are y′
No y′m′ exist
= No y′ are m′
= No m′ are y′