# Page:Carroll - Game of Logic.djvu/76

60
[Ch. III.
1.  ——
2.  0

7.
 1
It might be thought that the proper Diagram would be
 —— 1
, 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

[See pp. 40, 1]