Page:Carroll - Game of Logic.djvu/82

66 12. All $$y$$ are $$x$$, and all $$x^\prime$$ are $$y$$. i.e. All active boys are fat, and all thin ones are lazy.

13. No $$x$$ exist, and no $$y^\prime$$ exist. i.e. No cats have green eyes, and none have bad tempers.

14. Some $$x$$ are $$y^\prime$$, and some $$x^\prime$$ are $$y$$. Or, some $$y$$ are $$x^\prime$$, and some $$y^\prime$$ are $$x$$. i.e. Some green-eyed cats are bad-tempered, and some, that have not green eyes, are good-tempered. Or, some good-tempered cats have not green eyes, and some bad-tempered ones have green eyes.

15. Some $$x$$ are $$y$$, and no $$x^\prime$$ are $$y^\prime$$. Or, some $$y$$ are $$x$$, and no $$y^\prime$$ are $$x^\prime$$. i.e. Some green-eyed cats are good-tempered, and none, that are not green-eyed, are bad-tempered. Or, some good-tempered cats have green eyes, and none, that are bad-tempered, have not green eyes.

16. All $$x$$ are $$y^\prime$$, and all $$x^\prime$$ are $$y$$. Or, all $$y$$ are $$x^\prime$$, and all $$y^\prime$$ are $$x$$. i.e. All green-eyed cats are bad-tempered, and all, that have not green eyes, are good-tempered. Or, all good-tempered ones have eyes that are not green, and all bad-tempered ones have green eyes.