# Page:Carroll - Game of Logic.djvu/56

40
[Ch. II.
CROSS QUESTIONS.

§ 2. Half of Smaller Diagram.
Propositions to be represented.

 ${\displaystyle y}$ ${\displaystyle x}$${\displaystyle y^{\prime }}$

1. Some ${\displaystyle x}$ are not-${\displaystyle y}$.

2. All ${\displaystyle x}$ are not-${\displaystyle y}$.

3. Some ${\displaystyle x}$ are ${\displaystyle y}$, and some are not-${\displaystyle y}$.

4. No ${\displaystyle x}$ exist.

5. Some ${\displaystyle x}$ exist.

6. No ${\displaystyle x}$ are not-${\displaystyle y}$.

7. Some ${\displaystyle x}$ are not-${\displaystyle y}$, and some ${\displaystyle x}$ exist.

Taking ${\displaystyle x}$ = "judges"; ${\displaystyle y}$ = "just";

8. No judges are just.

9. Some judges are unjust.

10. All judges are just.

Taking ${\displaystyle x}$ = "plums"; ${\displaystyle y}$ = "wholesome";

11. Some plums are wholesome.

12. There are no wholesome plums.

13. Plums are some of them wholesome, and some not.

14. All plums are unwholesome.

[See pp. 59, 60]