# Page:Carroll - Game of Logic.djvu/97

§ 7.
81
BOTH DIAGRAMS EMPLOYED.
1.  0 0 0 1 0 1
 0 1 1

Let "food" be Universe; ${\displaystyle m}$ = "sweet"; ${\displaystyle x}$ = "sugar"; ${\displaystyle y}$ = "salt".

 All ${\displaystyle x}$ are ${\displaystyle m}$; All ${\displaystyle y}$ are ${\displaystyle m^{\prime }}$. ${\displaystyle \scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}}$ ∴ ${\displaystyle \scriptstyle {\left\{{\begin{matrix}\ \\\ \end{matrix}}\right.}}$ All ${\displaystyle x}$ are ${\displaystyle y^{\prime }}$. All ${\displaystyle y}$ are ${\displaystyle x^{\prime }}$.
 i.e. ${\displaystyle \scriptstyle {\left\{{\begin{matrix}\ \\\ \end{matrix}}\right.}}$ Sugar is not salt. Salt is not sugar.
2.  1 0 0
 1

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

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

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

[See p. 53]