# Page:Carroll - Game of Logic.djvu/80

64
[Ch. III. § 4.

16. Some ${\displaystyle y}$ are ${\displaystyle x}$, and all ${\displaystyle x}$ are ${\displaystyle y}$. i.e.
 1 0 0

17. No ${\displaystyle x^{\prime }}$ exist. i.e.
 0 0

18. All ${\displaystyle x}$ are ${\displaystyle y^{\prime }}$. i.e.
 0 1

19. No ${\displaystyle x}$ are ${\displaystyle y}$. i.e.
 0

20. Some ${\displaystyle x^{\prime }}$ are ${\displaystyle y}$, and some are ${\displaystyle y^{\prime }}$. i.e.
 1 1

21. No ${\displaystyle y}$ exist, and some ${\displaystyle x}$ exist. i.e.
 0 1 0

22. All ${\displaystyle x^{\prime }}$ are ${\displaystyle y}$, and all ${\displaystyle y^{\prime }}$ are ${\displaystyle x}$. i.e.
 1 1 0

23. Some ${\displaystyle x}$ are ${\displaystyle y}$, and some ${\displaystyle x^{\prime }}$ are ${\displaystyle y^{\prime }}$. i.e.
 1 1

[See p. 45]