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Revision as of 15:56, 22 January 2009
, 15:56, 22 January 2009→Table Stuff
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</pre>
</pre>
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:96%"
|+ '''Table 6. Propositional Forms on One Variable'''
|- style="background:ghostwhite"
| style="width:16%" |
<math>\begin{matrix}\mathcal{L}_1 \\ \mbox{Decimal}\end{matrix}</math>
| style="width:16%" |
<math>\begin{matrix}\mathcal{L}_2 \\ \mbox{Binary}\end{matrix}</math>
| style="width:16%" |
<math>\begin{matrix}\mathcal{L}_3 \\ \mbox{Vector}\end{matrix}</math>
| style="width:16%" |
<math>\begin{matrix}\mathcal{L}_4 \\ \mbox{Cactus}\end{matrix}</math>
| style="width:16%" |
<math>\begin{matrix}\mathcal{L}_5 \\ \mbox{English}\end{matrix}</math>
| style="width:16%" |
<math>\begin{matrix}\mathcal{L}_6 \\ \mbox{Ordinary}\end{matrix}</math>
|- style="background:ghostwhite"
| <math>~</math>
| align="right" | <math>x\colon\!</math>
| <math>1~0</math>
| <math>~</math>
| <math>~</math>
| <math>~</math>
|-
| <math>f_0\!</math>
| <math>f_{00}\!</math>
| <math>0~0</math>
| <math>(~)\!</math>
| <math>\mbox{false}\!</math>
| <math>0\!</math>
|-
| <math>f_1\!</math>
| <math>f_{01}\!</math>
| <math>0~1</math>
| <math>(x)\!</math>
| <math>\mbox{not}\ x</math>
| <math>\lnot x</math>
|-
| <math>f_2\!</math>
| <math>f_{10}\!</math>
| <math>1~0</math>
| <math>x\!</math>
| <math>x\!</math>
| <math>x\!</math>
|-
| <math>f_3\!</math>
| <math>f_{11}\!</math>
| <math>1~1</math>
| <math>((~))\!</math>
| <math>\mbox{true}\!</math>
| <math>1\!</math>
|}
<br>
<br>
o----------o----------o----------o----------o----------o----------o----------o
o----------o----------o----------o----------o----------o----------o----------o
</pre>
</pre>
<br>
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:96%"
|+ '''Table 7. Propositional Forms on Two Variables'''
|- style="background:ghostwhite"
| style="width:16%" |
<math>\begin{matrix}\mathcal{L}_1 \\ \mbox{Decimal}\end{matrix}</math>
| style="width:16%" |
<math>\begin{matrix}\mathcal{L}_2 \\ \mbox{Binary}\end{matrix}</math>
| style="width:16%" |
<math>\begin{matrix}\mathcal{L}_3 \\ \mbox{Vector}\end{matrix}</math>
| style="width:16%" |
<math>\begin{matrix}\mathcal{L}_4 \\ \mbox{Cactus}\end{matrix}</math>
| style="width:16%" |
<math>\begin{matrix}\mathcal{L}_5 \\ \mbox{English}\end{matrix}</math>
| style="width:16%" |
<math>\begin{matrix}\mathcal{L}_6 \\ \mbox{Ordinary}\end{matrix}</math>
|- style="background:ghostwhite"
| <math>~\!</math>
| align="right" | <math>x\colon\!</math>
| <math>1~1~0~0\!</math>
| <math>~\!</math>
| <math>~\!</math>
| <math>~\!</math>
|-
|- style="background:ghostwhite"
| <math>~\!</math>
| align="right" | <math>y\colon\!</math>
| <math>1~0~1~0\!</math>
| <math>~\!</math>
| <math>~\!</math>
| <math>~\!</math>
|-
| <math>f_{0}\!</math>
| <math>f_{0000}\!</math>
| <math>0~0~0~0\!</math>
| <math>(~)\!</math>
| <math>\mbox{false}\!</math>
| <math>0\!</math>
|-
| <math>f_{1}\!</math>
| <math>f_{0001}\!</math>
| <math>0~0~0~1\!</math>
| <math>(x)(y)\!</math>
| <math>\mbox{neither}\ x\ \mbox{nor}\ y\!</math>
| <math>\lnot x \land \lnot y\!</math>
|-
| <math>f_{2}\!</math>
| <math>f_{0010}\!</math>
| <math>0~0~1~0\!</math>
| <math>(x)\ y\!</math>
| <math>y\ \mbox{without}\ x\!</math>
| <math>\lnot x \land y\!</math>
|-
| <math>f_{3}\!</math>
| <math>f_{0011}\!</math>
| <math>0~0~1~1\!</math>
| <math>(x)\!</math>
| <math>\mbox{not}\ x\!</math>
| <math>\lnot x\!</math>
|-
| <math>f_{4}\!</math>
| <math>f_{0100}\!</math>
| <math>0~1~0~0\!</math>
| <math>x\ (y)\!</math>
| <math>x\ \mbox{without}\ y\!</math>
| <math>x \land \lnot y\!</math>
|-
| <math>f_{5}\!</math>
| <math>f_{0101}\!</math>
| <math>0~1~0~1\!</math>
| <math>(y)\!</math>
| <math>\mbox{not}\ y\!</math>
| <math>\lnot y\!</math>
|-
| <math>f_{6}\!</math>
| <math>f_{0110}\!</math>
| <math>0~1~1~0\!</math>
| <math>(x, y)\!</math>
| <math>x\ \mbox{not equal to}\ y\!</math>
| <math>x \ne y\!</math>
|-
| <math>f_{7}\!</math>
| <math>f_{0111}\!</math>
| <math>0~1~1~1\!</math>
| <math>(x\ y)\!</math>
| <math>\mbox{not both}\ x\ \mbox{and}\ y\!</math>
| <math>\lnot x \lor \lnot y\!</math>
|-
| <math>f_{8}\!</math>
| <math>f_{1000}\!</math>
| <math>1~0~0~0\!</math>
| <math>x\ y\!</math>
| <math>x\ \mbox{and}\ y\!</math>
| <math>x \land y\!</math>
|-
| <math>f_{9}\!</math>
| <math>f_{1001}\!</math>
| <math>1~0~0~1\!</math>
| <math>((x, y))\!</math>
| <math>x\ \mbox{equal to}\ y\!</math>
| <math>x = y\!</math>
|-
| <math>f_{10}\!</math>
| <math>f_{1010}\!</math>
| <math>1~0~1~0\!</math>
| <math>y\!</math>
| <math>y\!</math>
| <math>y\!</math>
|-
| <math>f_{11}\!</math>
| <math>f_{1011}\!</math>
| <math>1~0~1~1\!</math>
| <math>(x\ (y))\!</math>
| <math>\mbox{not}\ x\ \mbox{without}\ y\!</math>
| <math>x \Rightarrow y\!</math>
|-
| <math>f_{12}\!</math>
| <math>f_{1100}\!</math>
| <math>1~1~0~0\!</math>
| <math>x\!</math>
| <math>x\!</math>
| <math>x\!</math>
|-
| <math>f_{13}\!</math>
| <math>f_{1101}\!</math>
| <math>1~1~0~1\!</math>
| <math>((x)\ y)\!</math>
| <math>\mbox{not}\ y\ \mbox{without}\ x\!</math>
| <math>x \Leftarrow y\!</math>
|-
| <math>f_{14}\!</math>
| <math>f_{1110}\!</math>
| <math>1~1~1~0\!</math>
| <math>((x)(y))\!</math>
| <math>x\ \mbox{or}\ y\!</math>
| <math>x \lor y\!</math>
|-
| <math>f_{15}\!</math>
| <math>f_{1111}\!</math>
| <math>1~1~1~1\!</math>
| <math>((~))\!</math>
| <math>\mbox{true}\!</math>
| <math>1\!</math>
|}
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