, "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.

pg035
TABLE III.

.-------------------------------------------------------------.
| | .-------. | | .-------. |
| Some xy exist | |(.)| | | | |(.)|( )| |
| = Some x are y | |---|---| | All x are y | |---|---| |
| = Some y are x | | | | | | | | | |
| | .-------. | | .-------. |
|------------------|-----------|------------------|-----------|
| | .-------. | | .-------. |
| Some xy' exist | | |(.)| | | |( )|(.)| |
| = Some x are y' | |---|---| | All x are y' | |---|---| |
| = Some y' are x | | | | | | | | | |
| | .-------. | | .-------. |
|------------------|-----------|------------------|-----------|
| | .-------. | | .-------. |
| Some x'y exist | | | | | | | | | |
| = Some x' are y | |---|---| | All x' are y | |---|---| |
| = Some y are x' | |(.)| | | | |(.)|( )| |
| | .-------. | | .-------. |
|------------------|-----------|------------------|-----------|
| | .-------. | | .-------. |
| Some x'y' exist | | | | | | | | | |
| = Some x' are y'| |---|---| | All x' are y' | |---|---| |
| = Some y' are x'| | |(.)| |