# Page:Carroll - Game of Logic.djvu/33

§ 1.]
17
PROPOSITIONS.

This tells us, with regard to the ${\displaystyle xy^{\prime }}$-Square, that it is wholly 'empty', since both compartments are so marked. With regard to the ${\displaystyle xy}$-Square, it tells us that it is 'occupied'. True, it is only one compartment of it that is so marked; but that is quite enough, whether the other be 'occupied' or 'empty', to the fact that there is something in the Square.

If, then, we transfer our marks to the smaller Diagram, so as to get rid of the ${\displaystyle xy^{\prime }}$-subdivisions, we have a right to mark it

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which means, you know, "all ${\displaystyle x}$ are ${\displaystyle y}$."

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

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Once more: how shall we interpret this, with regard to ${\displaystyle x}$ and ${\displaystyle y}$?

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This tells us, as to the ${\displaystyle xy}$-Square, that one of its compartments is 'empty'. But this information is