# Page:Carroll - Game of Logic.djvu/78

62
[Ch. III.

8. No ${\displaystyle x}$ are ${\displaystyle y}$. i. e. No good riddles are hard.

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

10. No ${\displaystyle x}$ are ${\displaystyle y}$. i. e. No lobsters are selfish.

11. All ${\displaystyle x}$ are ${\displaystyle y^{\prime }}$. i. e. All lobsters are unselfish.

12. Some ${\displaystyle x}$ are ${\displaystyle y}$, and some are ${\displaystyle y^{\prime }}$. i. e. Some lobsters are selfish, and some are unselfish.

13. All ${\displaystyle y^{\prime }}$ are ${\displaystyle x^{\prime }}$. i. e. All invalids are unhappy.

14. Some ${\displaystyle y^{\prime }}$ exist, i. e. Some people are unhealthy.

15. Some ${\displaystyle y^{\prime }}$ are ${\displaystyle x}$, and some are ${\displaystyle x^{\prime }}$. i. e. Some invalids are happy, and some are unhappy.

16. No ${\displaystyle y^{\prime }}$ exist. i. e. Nobody is unhealthy.

§ 4. Smaller Diagram.
Propositions represented.

1.  1 0
2.  1
3.  0
4.  1

[See pp. 42–4]