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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 13:14, 4 May 2009
, 13:14, 4 May 2009→Example 6
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
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<math>\begin{array}{*{14}{c}}
<math>\begin{array}{*{15}{c}}
X & = & \{ & a, & b, & c, & d, & e, & f, & g, & h, & i & \}
X & = & \{ & a, & b, & c, & d, & e, & f, & g, & h, & i & \}
\\[6pt]
\\[6pt]
W & = & \{ & d, & f & \}
W & = & \{ & d, & f & \}
\\[6pt]
\\[6pt]
L & = & \{ & b\!:\!a, & b\!:\!c, & c\!:\!b, & c\!:\!d, & e\!:\!d, & e\!:\!f, & g\!:\!f, & g\!:\!h, & h\!:\!g, & h\!:\!i & \}
L & = & \{ & b\!:\!a, & b\!:\!c, & c\!:\!b, & c\!:\!d, & e\!:\!d, & e\!:\!e, & e\!:\!f, & g\!:\!f, & g\!:\!h, & h\!:\!g, & h\!:\!i & \}
\end{array}</math>
\end{array}</math>
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o o o o o o o o o X
o o o o o o o o o X
\ \ / / \ / \ \ / /
\ \ / / \ | / \ \ / /
\ \ / \ / \ \ / L
\ \ / \ | / \ \ / L
\ / \ / \ / \ / \ /
\ / \ / \|/ \ / \ /
o o o o o o o o o X
o o o o o o o o o X
a b c d e f g h i
a b c d e f g h i
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
| <math>(\mathfrak{L}^\mathfrak{W})_e ~=~ \prod_{x \in X} \mathfrak{L}_{ex}^{\mathfrak{W}_x} ~=~ 0^0 \cdot 0^0 \cdot 0^0 \cdot 1^0 \cdot 0^0 \cdot 1^0 \cdot 0^0 \cdot 0^0 \cdot 0^0 ~=~ 1</math>
| <math>(\mathfrak{L}^\mathfrak{W})_e ~=~ \prod_{x \in X} \mathfrak{L}_{ex}^{\mathfrak{W}_x} ~=~ 0^0 \cdot 0^0 \cdot 0^0 \cdot 1^1 \cdot 1^0 \cdot 1^1 \cdot 0^0 \cdot 0^0 \cdot 0^0 ~=~ 1</math>
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