Page:Carroll - Game of Logic.djvu/81

§ 5. Smaller Diagram.
Symbols interpreted.

 

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1. Some $y$ are not-$x$,
or, Some not-$x$ are $y$.

2. No not-$x$ are not-$y$,
or, No not-$y$ are not-$x$.

3. No not-$y$ are $x$.

4. No not-$x$ exist. i.e. No Things are not-$x$.

5. No $y$ exist. i.e. No houses are two-storied.

6. Some $x^{\prime }$ exist. i.e. Some houses are not built of brick.

7. No $x$ are $y^{\prime }$. Or, no $y^{\prime }$ are $x$. i.e. No houses, built of brick, are other than two-storied. Or, no houses, that are not two-storied, are built of brick.

8. All $x^{\prime }$ are $y^{\prime }$. i.e. All houses, that are not built of brick, are not two-storied.

9. Some $x$ are $y$, and some are $y^{\prime }$. i.e. Some fat boys are active, and some are not.

10. All $y^{\prime }$ are $x^{\prime }$. i.e. All lazy boys are thin.

11. All $x$ are $y^{\prime }$, and all $y^{\prime }$ are x. i.e. All fat boys are lazy, and all lazy ones are fat.

[See pp. 46, 7]