# Work ䷋

## Peirce’s 1870 “Logic of Relatives” • Comment 10.11

### HTML + LaTeX

#### Display 1

$\begin{array}{*{15}{c}} \mathbf{1} & = & \mathrm{B} & +\!\!, & \mathrm{C} & +\!\!, & \mathrm{D} & +\!\!, & \mathrm{E} & +\!\!, & \mathrm{I} & +\!\!, & \mathrm{J} & +\!\!, & \mathrm{O} \\[6pt] \mathrm{b} & = & \mathrm{O} \\[6pt] \mathrm{m} & = & \mathrm{C} & +\!\!, & \mathrm{I} & +\!\!, & \mathrm{J} & +\!\!, & \mathrm{O} \\[6pt] \mathrm{r} & = & \mathrm{D} & +\!\!, & \mathrm{O} \end{array}$

#### Display 2

$\begin{array}{*{15}{c}} \mathbf{1,} & = & \mathrm{B\!:\!B} & +\!\!, & \mathrm{C\!:\!C} & +\!\!, & \mathrm{D\!:\!D} & +\!\!, & \mathrm{E\!:\!E} & +\!\!, & \mathrm{I\!:\!I} & +\!\!, & \mathrm{J\!:\!J} & +\!\!, & \mathrm{O\!:\!O} \\[6pt] \mathrm{b,} & = & \mathrm{O\!:\!O} \\[6pt] \mathrm{m,} & = & \mathrm{C\!:\!C} & +\!\!, & \mathrm{I\!:\!I} & +\!\!, & \mathrm{J\!:\!J} & +\!\!, & \mathrm{O\!:\!O} \\[6pt] \mathrm{r,} & = & \mathrm{D\!:\!D} & +\!\!, & \mathrm{O\!:\!O} \end{array}$

#### Display 3

$\begin{array}{*{9}{c}} \mathbf{1,\!,} & = & \mathrm{B\!:\!B\!:\!B} & +\!\!, & \mathrm{C\!:\!C\!:\!C} & +\!\!, & \mathrm{D\!:\!D\!:\!D} & +\!\!, & \mathrm{E\!:\!E\!:\!E} \\ & & & +\!\!, & \mathrm{I\!:\!I\!:\!I} & +\!\!, & \mathrm{J\!:\!J\!:\!J} & +\!\!, & \mathrm{O\!:\!O\!:\!O} \\[6pt] \mathrm{b,\!,} & = & \mathrm{O\!:\!O\!:\!O} \\[6pt] \mathrm{m,\!,} & = & \mathrm{C\!:\!C\!:\!C} & +\!\!, & \mathrm{I\!:\!I\!:\!I} & +\!\!, & \mathrm{J\!:\!J\!:\!J} & +\!\!, & \mathrm{O\!:\!O\!:\!O} \\[6pt] \mathrm{r,\!,} & = & \mathrm{D\!:\!D\!:\!D} & +\!\!, & \mathrm{O\!:\!O\!:\!O} \end{array}$

#### Display 4

$\begin{array}{lll} \mathrm{m,\!b,\!r} & = & (\mathrm{C\!:\!C} ~+\!\!,~ \mathrm{I\!:\!I} ~+\!\!,~ \mathrm{J\!:\!J} ~+\!\!,~ \mathrm{O\!:\!O})(\mathrm{O\!:\!O})(\mathrm{D} ~+\!\!,~ \mathrm{O}) \\[6pt] & = & (\mathrm{C\!:\!C} ~+\!\!,~ \mathrm{I\!:\!I} ~+\!\!,~ \mathrm{J\!:\!J} ~+\!\!,~ \mathrm{O\!:\!O})(\mathrm{O}) \\[6pt] & = & \mathrm{O} \end{array}$

#### Display 5

$\begin{array}{lll} \mathrm{m,\!,\!b,\!r} & = & (\mathrm{C\!:\!C\!:\!C} ~+\!\!,~ \mathrm{I\!:\!I\!:\!I} ~+\!\!,~ \mathrm{J\!:\!J\!:\!J} ~+\!\!,~ \mathrm{O\!:\!O\!:\!O})(\mathrm{O\!:\!O})(\mathrm{D} ~+\!\!,~ \mathrm{O}) \\[6pt] & = & (\mathrm{O\!:\!O\!:\!O})(\mathrm{O\!:\!O})(\mathrm{O}) \\[6pt] & = & \mathrm{O} \end{array}$

#### Display 6

$\begin{array}{l} \mathbf{1},\!, = \mathrm{B\!:\!B\!:\!B} ~+\!\!,~ \mathrm{C\!:\!C\!:\!C} ~+\!\!,~ \mathrm{D\!:\!D\!:\!D} ~+\!\!,~ \mathrm{E\!:\!E\!:\!E} ~+\!\!,~ \mathrm{I\!:\!I\!:\!I} ~+\!\!,~ \mathrm{J\!:\!J\!:\!J} ~+\!\!,~ \mathrm{O\!:\!O\!:\!O} \end{array}$