# Page:Carroll - Game of Logic.djvu/82

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[Ch. III. § 5.

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.

[See p. 47] 