Page:Carroll - Game of Logic.djvu/76

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7.  It might be thought that the proper Diagram would be , in order to express "some $$x$$ exist": but this is really contained in "some $$x$$ are $y^\prime$." To put a red counter on the division-line would only tell us "one of the two compartments is occupied", which we know already, in knowing that one is occupied.

8. No $$x$$ are $y$. i.e.

9. Some $$x$$ are $y^\prime$. i.e.

10. All $$x$$ are $y$. i.e.

11. Some $$x$$ are $y$. i.e.

12. No $$x$$ are $y$. i.e.

13. Some $$x$$ are $y$, and some are $y^\prime$. i.e.

14. All $$x$$ are $y^\prime$. i.e.

15. No $$y$$ are $x^\prime$. i.e.