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

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[Ch. III. § 5.
12. All ${\displaystyle y}$ are ${\displaystyle x}$, and all ${\displaystyle x^{\prime }}$ are ${\displaystyle y}$. i.e. All active boys are fat, and all thin ones are lazy.
13. No ${\displaystyle x}$ exist, and no ${\displaystyle y^{\prime }}$ exist. i.e. No cats have green eyes, and none have bad tempers.
14. Some ${\displaystyle x}$ are ${\displaystyle y^{\prime }}$, and some ${\displaystyle x^{\prime }}$ are ${\displaystyle y}$. Or, some ${\displaystyle y}$ are ${\displaystyle x^{\prime }}$, and some ${\displaystyle y^{\prime }}$ are ${\displaystyle x}$. 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 ${\displaystyle x}$ are ${\displaystyle y}$, and no ${\displaystyle x^{\prime }}$ are ${\displaystyle y^{\prime }}$. Or, some ${\displaystyle y}$ are ${\displaystyle x}$, and no ${\displaystyle y^{\prime }}$ are ${\displaystyle x^{\prime }}$. 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 ${\displaystyle x}$ are ${\displaystyle y^{\prime }}$, and all ${\displaystyle x^{\prime }}$ are ${\displaystyle y}$. Or, all ${\displaystyle y}$ are ${\displaystyle x^{\prime }}$, and all ${\displaystyle y^{\prime }}$ are ${\displaystyle x}$. 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.