[Note that the Subject of the given Proposition settles which Half we are to use; and that its Predicate settles in which portion of that Half we are to place the Red Counter.]
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Similarly we may represent the seven similar Propositions “All x are y′”, “All x′ are y”, “All x′ are y′”, “All y are x”, “All y are x′”, “All y′ are x”, and “All y′ are x′”.
Let us take, lastly, the Double Proposition “Some x are y and some are y′”, each part of which we already know how to represent.
Similarly we may represent the three similar Propositions, “Some x′ are y and some are y′”, “Some y are x and some are x′”, “Some y′ are x and some are x′”.
The Reader should now get his genial friend to question him, severely, on these two Tables. The Inquisitor should have the Tables before him: but the Victim should have nothing but a blank Diagram, and the Counters with which he is to represent the various Propositions named by his friend, e.g. “Some y exist”, “No y′ are x”, “All x are y”, &c. &c.
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