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Revision as of 22:08, 11 September 2013
, 22:08, 11 September 2013update
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Line 6,402:
<font face="courier new">+| ←+| ''F'' = ‹''f'' , ''g''›+| ←
−|}
−{| align="right" style="background:ghostwhite; text-align:right"+| ''u'' =
| 1 1 0 0+|}+|+{| align="left" style="background:ghostwhite; text-align:left"+| = ''u''+|-+| = ''v''+| rowspan="2" | ''f''<sub>''j''</sub>‹''u'', ''v''›+|- style="background:ghostwhite"+|+| ''x'' =+|-+| ''y'' =+|}+|+| 1 1 1 0+|-+| 1 0 0 1+|}+|+| = ''f''‹''u'', ''v''›+|-+| = ''g''‹''u'', ''v''›+|}+|-+|+| ''f''<sub>0</sub>+|-+| ''f''<sub>1</sub>+|-+| ''f''<sub>2</sub>+|-+| ''f''<sub>3</sub>+|-+| ''f''<sub>4</sub>+|-+| ''f''<sub>5</sub>+|-+| ''f''<sub>6</sub>+|-+| ''f''<sub>7</sub>+|}+|+| ()+|-+| (''x'')(''y'') +|-+| (''x'') ''y'' +|-+| (''x'') +|-+| ''x'' (''y'') +|-+| (''y'') +|-+| (''x'', ''y'') +|-+| (''x'' ''y'') +|}+|+| 0 0 0 0+|-+| 0 0 0 1+|-+| 0 0 1 0+|-+| 0 0 1 1+|-+| 0 1 0 0+|-+| 0 1 0 1+|-+| 0 1 1 0+|-+| 0 1 1 1+|}+|+| ()+|-+| ()+|-+| (''u'')(''v'') +|-
−| (''u'')(''v'')
−|-
−| (''u'', ''v'')
−|-
−| (''u'', ''v'')
−|-
−| (''u'' ''v'')
−|-
−| (''u'' ''v'')
−|}
−|
−| ''f''<sub>0</sub>
−|-
−| ''f''<sub>0</sub>
−|-
−| ''f''<sub>1</sub>
−|-
−| ''f''<sub>1</sub>
−|-
−| ''f''<sub>6</sub>
−|-
−| ''f''<sub>6</sub>
−|-
−| ''f''<sub>7</sub>
−| ''f''<sub>7</sub>
−|}
−|-
−|
−{| cellpadding="2"
−|-
−| ''f''<sub>9</sub>
−|-
−| ''f''<sub>10</sub>
−|-
−| ''f''<sub>11</sub>
−|-
−| ''f''<sub>12</sub>
−|-
−| ''f''<sub>13</sub>
−|-
−| ''f''<sub>14</sub>
−|-
−| ''f''<sub>15</sub>
−|}
−|
−| ''x'' ''y''
−|-
−| ((''x'', ''y''))
−|-
−| ''y''
−|-
−| (''x'' (''y''))
−|-
−| ''x''
−|-
−| ((''x'') ''y'')
−|-
−| ((''x'')(''y''))
−|-
−| (())
−|}
−{| cellpadding="2"
−| 1 0 0 0
−|-
−| 1 0 0 1
−|-
−| 1 0 1 0
−|-
−| 1 0 1 1
−|-
−| 1 1 0 0
−|-
−| 1 1 0 1
−|-
−| 1 1 1 0
−|-
−| 1 1 1 1
−|}
−{| cellpadding="2"
−| ''u'' ''v''
−|-
−| ''u'' ''v''
−|-
−| ((''u'', ''v''))
−|-
−| ((''u'', ''v''))
−|-
−| ((''u'')(''v''))
−|-
−| ((''u'')(''v''))
−|-
−| (())
−|-
−| (())
−|}
−{| cellpadding="2"
−| ''f''<sub>8</sub>
−|-
−| ''f''<sub>8</sub>
−|-
−| ''f''<sub>9</sub>
−|-
−| ''f''<sub>9</sub>
−|-
−| ''f''<sub>14</sub>
−|-
−| ''f''<sub>14</sub>
−|-
−| ''f''<sub>15</sub>
−|-
−| ''f''<sub>15</sub>
−|}
</font>
<br>
<br>
−{| align="center" cellpadding="6" cellspacing="0" style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; text-align:center; width:90%"
+{| align="center" cellpadding="6" cellspacing="0" style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; text-align:center; width:80%"
|+ style="height:30px" | <math>\text{Table 64.} ~~ \text{A Transformation of Positions}\!</math>
|+ style="height:30px" | <math>\text{Table 64.} ~~ \text{A Transformation of Positions}\!</math>
|- style="height:40px; background:ghostwhite; width:100%"
|- style="height:40px; background:ghostwhite; width:100%"
−| style="width:10%" | <math>u\!</math>
+| style="width:8%" | <math>u\!</math>
−| style="width:10%" | <math>v\!</math>
+| style="width:8%" | <math>v\!</math>
| style="width:12%; border-left:1px solid black" | <math>x\!</math>
| style="width:12%; border-left:1px solid black" | <math>x\!</math>
| style="width:12%" | <math>y\!</math>
| style="width:12%" | <math>y\!</math>
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| style="width:10%" | <math>\texttt{(} x \texttt{)} y\!</math>
| style="width:10%" | <math>\texttt{(} x \texttt{)} y\!</math>
| style="width:10%" | <math>\texttt{(} x \texttt{)(} y \texttt{)}\!</math>
| style="width:10%" | <math>\texttt{(} x \texttt{)(} y \texttt{)}\!</math>
−| style="width:16%; border-left:1px solid black" | <math>X^\bullet = [x, y]\!</math>
+| style="width:20%; border-left:1px solid black" | <math>X^\bullet = [x, y]\!</math>
|-
|-
| style="border-top:1px solid black" |
| style="border-top:1px solid black" |
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Line 6,523:
<br>
<br>
−{| align="center" border="1" cellpadding="6" cellspacing="0" style="text-align:center; width:80%"
−{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:90%"
+|+ style="height:30px" | <math>\text{Table 65-a.} ~~ \text{Induced Transformation on Propositions}\!</math>
−|+ '''Table 65. Induced Transformation on Propositions'''
+|- style="height:50px; background:ghostwhite"
+| style="width:20%" | <math>X^\bullet~\!</math>
+| style="width:20%; border-right:none" | <math>\longleftarrow\!</math>
+| style="width:20%; border-left:none; border-right:none" | <math>F = (f, g)\!</math>
+| style="width:20%; border-left:none" | <math>\longleftarrow\!</math>
+| style="width:20%" | <math>U^\bullet~\!</math>
|- style="background:ghostwhite"
|- style="background:ghostwhite"
−| ''X''<sup> •</sup>
+| rowspan="2" | <math>f_i (x, y)\!</math>
−| colspan="3" |
+| align="right" | <math>\begin{matrix}u = \\ v =\end{matrix}</math>
−{| align="center" border="0" cellpadding="4" cellspacing="0" style="background:ghostwhite; font-weight:bold; text-align:center; width:80%"
+| <math>\begin{matrix}1~1~0~0\\1~0~1~0\end{matrix}</math>
−| align="left" | <math>\begin{matrix}= u \\ = v\end{matrix}</math>
−| rowspan="2" style="width:20%" | <math>f_j (u, v)\!</math>
−| ''U''<sup> •</sup>
|- style="background:ghostwhite"
|- style="background:ghostwhite"
−| rowspan="2" | ''f''<sub>''i''</sub>‹''x'', ''y''›
+| align="right" | <math>\begin{matrix}x = \\ y =\end{matrix}</math>
−|
+| <math>\begin{matrix}1~1~1~0\\1~0~0~1\end{matrix}</math>
−| align="left" | <math>\begin{matrix}= f(u, v) \\ = g(u, v)\end{matrix}</math>
−|-
|-
−| ''v'' =
+| valign="bottom" |
−|}
+<math>\begin{matrix}
−|
+f_{0}
−{| align="center" style="background:ghostwhite; text-align:center"
+\\[2pt]
−f_{1}
+\\[2pt]
+f_{2}
+\\[2pt]
+f_{3}
+\\[2pt]
+f_{4}
+\\[2pt]
+f_{5}
+\\[2pt]
+f_{6}
+\\[2pt]
+f_{7}
+\end{matrix}</math>
+| valign="bottom" |
+<math>\begin{matrix}
+\texttt{(~)}
+\\[2pt]
+\texttt{(} x \texttt{)(} y \texttt{)}
+\\[2pt]
+\texttt{(} x \texttt{)~} y \texttt{~}
+\\[2pt]
+\texttt{(} x \texttt{)~~~}
+\\[2pt]
+\texttt{~} x \texttt{~(} y \texttt{)}
+\\[2pt]
+\texttt{~~~(} y \texttt{)}
+\\[2pt]
+\texttt{(} x \texttt{,~} y \texttt{)}
+\\[2pt]
+\texttt{(} x \texttt{~~} y \texttt{)}
+\end{matrix}</math>
+| valign="bottom" |
+<math>\begin{matrix}
+0~0~0~0
+\\[2pt]
+0~0~0~1
+\\[2pt]
+0~0~1~0
+\\[2pt]
+0~0~1~1
+\\[2pt]
+0~1~0~0
+\\[2pt]
+0~1~0~1
+\\[2pt]
+0~1~1~0
+\\[2pt]
+0~1~1~1
+\end{matrix}</math>
+| valign="bottom" |
+<math>\begin{matrix}
+\texttt{(~)}
+\\[2pt]
+\texttt{(~)}
+\\[2pt]
+\texttt{(} u \texttt{)(} v \texttt{)}
+\\[2pt]
+\texttt{(} u \texttt{)(} v \texttt{)}
+\\[2pt]
+\texttt{(} u \texttt{,~} v \texttt{)}
+\\[2pt]
+\texttt{(} u \texttt{,~} v \texttt{)}
+\\[2pt]
+\texttt{(} u \texttt{~~} v \texttt{)}
+\\[2pt]
+\texttt{(} u \texttt{~~} v \texttt{)}
+\end{matrix}\!</math>
+| valign="bottom" |
+<math>\begin{matrix}
+f_{0}
+\\[2pt]
+f_{0}
+\\[2pt]
+f_{1}
+\\[2pt]
+f_{1}
+\\[2pt]
+f_{6}
+\\[2pt]
+f_{6}
+\\[2pt]
+f_{7}
+\\[2pt]
+f_{7}
+\end{matrix}</math>
|-
|-
−| 1 0 1 0
+| valign="bottom" |
−<math>\begin{matrix}
−f_{8}
−\\[2pt]
−f_{9}
−\\[2pt]
−f_{10}
−|}
+\\[2pt]
−f_{11}
−\\[2pt]
−f_{12}
−{| align="right" style="background:ghostwhite; text-align:right"
+\\[2pt]
−f_{13}
−\\[2pt]
−f_{14}
−\\[2pt]
−f_{15}
−{| align="center" style="background:ghostwhite; text-align:center"
+\end{matrix}</math>
−| valign="bottom" |
−<math>\begin{matrix}
−\texttt{~~} x \texttt{~~} y \texttt{~~}
−\\[2pt]
−\texttt{((} x \texttt{,~} y \texttt{))}
−{| align="left" style="background:ghostwhite; text-align:left"
+\\[2pt]
−\texttt{~~~~~} y \texttt{~~}
−\\[2pt]
−\texttt{~(} x \texttt{~(} y \texttt{))}
−\\[2pt]
−\texttt{~~} x \texttt{~~~~~}
−\\[2pt]
−{| cellpadding="2"
+\texttt{((} x \texttt{)~} y \texttt{)~}
−\\[2pt]
−\texttt{((} x \texttt{)(} y \texttt{))}
−\\[2pt]
−\texttt{((~))}
−\end{matrix}</math>
−| valign="bottom" |
−<math>\begin{matrix}
−1~0~0~0
−\\[2pt]
−1~0~0~1
−\\[2pt]
−1~0~1~0
−\\[2pt]
−1~0~1~1
−\\[2pt]
−1~1~0~0
−\\[2pt]
−{| cellpadding="2"
+1~1~0~1
−\\[2pt]
−1~1~1~0
−\\[2pt]
−1~1~1~1
−\end{matrix}</math>
−| valign="bottom" |
−<math>\begin{matrix}
−\texttt{~~} u \texttt{~~} v \texttt{~~}
−\\[2pt]
−\texttt{~~} u \texttt{~~} v \texttt{~~}
−\\[2pt]
−\texttt{((} u \texttt{,~} v \texttt{))}
−\\[2pt]
−\texttt{((} u \texttt{,~} v \texttt{))}
−\\[2pt]
−\texttt{((} u \texttt{)(} v \texttt{))}
−\\[2pt]
−{| cellpadding="2"
+\texttt{((} u \texttt{)(} v \texttt{))}
−\\[2pt]
−\texttt{((~))}
−\\[2pt]
−\texttt{((~))}
−\end{matrix}</math>
−| valign="bottom" |
−<math>\begin{matrix}
−f_{8}
−\\[2pt]
−f_{8}
−\\[2pt]
−f_{9}
−\\[2pt]
−f_{9}
−\\[2pt]
−f_{14}
−\\[2pt]
−{| cellpadding="2"
+f_{14}
−\\[2pt]
−f_{15}
−\\[2pt]
−f_{15}
−\end{matrix}</math>
−{| cellpadding="2"
−|-
−| ''f''<sub>8</sub>
−{| cellpadding="2"
−|
−|
−|
−|}
|}
−<br>
<br>
