Page:Carroll - Game of Logic.djvu/97

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    Let "food" be Universe; $m$ = "sweet"; $x$ = "sugar"; $y$ = "salt".

    All $x$ are $m$; All $y$ are $m^{\prime }$.

    $\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}$

    ∴

    $\scriptstyle {\left\{{\begin{matrix}\ \\\ \end{matrix}}\right.}$

    All $x$ are $y^{\prime }$. All $y$ are $x^{\prime }$.

    i.e.

    $\scriptstyle {\left\{{\begin{matrix}\ \\\ \end{matrix}}\right.}$

    Sugar is not salt. Salt is not sugar.

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    Let "Things" be Universe; $m$ = "eggs"; $x$ = "hard-boiled"; $y$ = "crackable".

    Some $m$ are $x$; No $m$ are $y^{\prime }$.

    $\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}$

    ∴ Some $x$ are $y$.

    i.e. Some hard-boiled things can be cracked.

[See p. 53]