# Page:Carroll - Game of Logic.djvu/99

§ 7.
83
BOTH DIAGRAMS EMPLOYED.
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Let "persons" be Universe; ${\displaystyle m}$ = "Jews"; ${\displaystyle x}$ = "mad"; ${\displaystyle y}$ = "Rabbis".

 No ${\displaystyle m}$ are ${\displaystyle x}$; All ${\displaystyle y}$ are ${\displaystyle m}$. ${\displaystyle \scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}}$ ∴ All ${\displaystyle y}$ are ${\displaystyle x^{\prime }}$.

i.e. All Rabbis are sane.

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Let "Things" be Universe; ${\displaystyle m}$ = "fish"; ${\displaystyle x}$ = "that can swim"; ${\displaystyle y}$ = "skates".

 No ${\displaystyle m}$ are ${\displaystyle x^{\prime }}$; Some ${\displaystyle y}$ are ${\displaystyle m}$. ${\displaystyle \scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}}$ ∴ Some ${\displaystyle y}$ are ${\displaystyle x}$.

i.e. Some skates can swim.

[See p. 54]