Page:Carroll - Game of Logic.djvu/81

III. § 5.]

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]