Page:Carroll - Game of Logic.djvu/76

7.

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It might be thought that the proper Diagram would be

——

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, in order to express "some ${\displaystyle x}$ exist": but this is really contained in "some ${\displaystyle x}$ are ${\displaystyle y^{\prime }}$." 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 ${\displaystyle x}$ are ${\displaystyle y}$. i.e.

0

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

1

10. All ${\displaystyle x}$ are ${\displaystyle y}$. i.e.

1

0

11. Some ${\displaystyle x}$ are ${\displaystyle y}$. i.e.

1

12. No ${\displaystyle x}$ are ${\displaystyle y}$. i.e.

0

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

1

1

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

0

1

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

0