The Game of Logic

by Lewis Carroll

which means, you know, "all x are y."

The result would have been exactly the same, if the given oblong had been marked thus:--

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

Once more: how shall we interpret this, with regard to x and y?

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

This tells us, as to the xy-Square, that ONE of its compartments is 'empty'. But this information is quite useless, as there is no mark in the OTHER compartment. If the other compartment happened to be 'empty' too, the Square would be 'empty': and, if it happened to be 'occupied', the Square would be 'occupied'. So, as we do not know WHICH is the case, we can say nothing about THIS Square.

The other Square, the xy'-Square, we know (as in the previous example) to be 'occupied'.

If, then, we transfer our marks to the smaller Diagram, we get merely this:--

-----------
| | |
| | 1 |
| | |
-----------

which means, you know, "some x are y'."