The Game of Logic

by Lewis Carroll

Let us take the negative portions first.

We have, then, to mark, on the larger Diagram, first, "no x are m", and secondly, "no y are m'". I think you will see, without further explanation, that the two results, separately, are

----------- -----------
| | | |0 | |
| --|-- | | --|-- |
| |0 | 0| | | | | | |
|--|--|--|--| |--|--|--|--|
| | | | | | | | | |
| --|-- | | --|-- |
| | | |0 | |
----------- -----------

and that these two, when combined, give us

-----------
|0 | |
| --|-- |
| |0 | 0| |
|--|--|--|--|
| | | | |
| --|-- |
|0 | |
-----------

We have now to mark the two positive portions, "some x are m'" and "some y are m".

The only two compartments, available for Things which are xm', are No. 9 and No. 10. Of these, No. 9 is already marked as 'empty'; so our red counter must go into No. 10.

Similarly, the only two, available for ym, are No. 11 and No. 13. Of these, No. 11 is already marked as 'empty'; so our red counter MUST go into No. 13.

The final result is

-----------
|0 | 1|
| --|-- |
| |0 | 0| |
|--|--|--|--|
| |1 | | |
| --|-- |
|0 | |
-----------