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The following Tables develop these ideas in more detail.
The following Tables develop these ideas in more detail.
<tr>
<tr>
<td width="4%" style="border-bottom:2px solid black" align="right">
<td width="4%" style="border-bottom:2px solid black" align="right">
<math>\begin{matrix}u\!:\\v\!:\end{matrix}</math></td>
<td width="6%" style="border-bottom:2px solid black">
<td width="6%" style="border-bottom:2px solid black">
<math>\begin{matrix}1100\\1010\end{matrix}</math></td>
<td width="10%" style="border-bottom:2px solid black; border-right:2px solid black">
<td width="10%" style="border-bottom:2px solid black; border-right:2px solid black">
<math>f</math></td>
<td width="10%" style="border-bottom:2px solid black">
<td width="10%" style="border-bottom:2px solid black">
<math>\texttt{(} \ell_{11} \texttt{)}</math><br>
<math>No ~ u</math><br>
<math>is ~ v</math></td>
<td width="10%" style="border-bottom:2px solid black">
<td width="10%" style="border-bottom:2px solid black">
<math>\texttt{(} \ell_{10} \texttt{)}</math><br>
<math>No ~ u</math><br>
<math>is ~ \texttt{(} v \texttt{)}</math></td>
<td width="10%" style="border-bottom:2px solid black">
<td width="10%" style="border-bottom:2px solid black">
<math>\texttt{(} \ell_{01} \texttt{)}</math><br>
<math>No ~ \texttt{(} u \texttt{)}</math><br>
<math>is ~ v</math></td>
<td width="10%" style="border-bottom:2px solid black">
<td width="10%" style="border-bottom:2px solid black">
<math>\texttt{(} \ell_{00} \texttt{)}</math><br>
<math>No ~ \texttt{(} u \texttt{)}</math><br>
<math>is ~ \texttt{(} v \texttt{)}</math></td>
<td width="10%" style="border-bottom:2px solid black">
<td width="10%" style="border-bottom:2px solid black">
<math>\ell_{00}</math><br>
<math>Some ~ \texttt{(} u \texttt{)}</math><br>
<math>is ~ \texttt{(} v \texttt{)}</math></td>
<td width="10%" style="border-bottom:2px solid black">
<td width="10%" style="border-bottom:2px solid black">
<math>\ell_{01}</math><br>
<math>Some ~ \texttt{(} u \texttt{)}</math><br>
<math>is ~ v</math></td>
<td width="10%" style="border-bottom:2px solid black">
<td width="10%" style="border-bottom:2px solid black">
<math>\ell_{10}</math><br>
<math>Some ~ u</math><br>
<math>is ~ \texttt{(} v \texttt{)}</math></td>
<td width="10%" style="border-bottom:2px solid black">
<td width="10%" style="border-bottom:2px solid black">
<math>\ell_{11}</math><br>
<math>Some ~ u</math><br>
<math>is ~ v</math></td></tr>
<tr>
<tr>
<tr>
<tr>
<td width="4%" style="border-bottom:2px solid black" align="right">
<td width="4%" style="border-bottom:2px solid black" align="right">
<math>\begin{matrix}u\!:\\v\!:\end{matrix}</math></td>
<td width="6%" style="border-bottom:2px solid black">
<td width="6%" style="border-bottom:2px solid black">
<math>\begin{matrix}1100\\1010\end{matrix}</math></td>
<td width="10%" style="border-bottom:2px solid black; border-right:2px solid black">
<td width="10%" style="border-bottom:2px solid black; border-right:2px solid black">
<math>f</math></td>
<td width="10%" style="border-bottom:2px solid black">
<td width="10%" style="border-bottom:2px solid black">
<math>\texttt{(} \ell_{11} \texttt{)}</math><br>
<math>No ~ u</math><br>
<math>is ~ v</math></td>
<td width="10%" style="border-bottom:2px solid black">
<td width="10%" style="border-bottom:2px solid black">
<math>\texttt{(} \ell_{10} \texttt{)}</math><br>
<math>No ~ u</math><br>
<math>is ~ \texttt{(} v \texttt{)}</math></td>
<td width="10%" style="border-bottom:2px solid black">
<td width="10%" style="border-bottom:2px solid black">
<math>\texttt{(} \ell_{01} \texttt{)}</math><br>
<math>No ~ \texttt{(} u \texttt{)}</math><br>
<math>is ~ v</math></td>
<td width="10%" style="border-bottom:2px solid black">
<td width="10%" style="border-bottom:2px solid black">
<math>\texttt{(} \ell_{00} \texttt{)}</math><br>
<math>No ~ \texttt{(} u \texttt{)}</math><br>
<math>is ~ \texttt{(} v \texttt{)}</math></td>
<td width="10%" style="border-bottom:2px solid black">
<td width="10%" style="border-bottom:2px solid black">
<math>\ell_{00}</math><br>
<math>Some ~ \texttt{(} u \texttt{)}</math><br>
<math>is ~ \texttt{(} v \texttt{)}</math></td>
<td width="10%" style="border-bottom:2px solid black">
<td width="10%" style="border-bottom:2px solid black">
<math>\ell_{01}</math><br>
<math>Some ~ \texttt{(} u \texttt{)}</math><br>
<math>is ~ v</math></td>
<td width="10%" style="border-bottom:2px solid black">
<td width="10%" style="border-bottom:2px solid black">
<math>\ell_{10}</math><br>
<math>Some ~ u</math><br>
<math>is ~ \texttt{(} v \texttt{)}</math></td>
<td width="10%" style="border-bottom:2px solid black">
<td width="10%" style="border-bottom:2px solid black">
<math>\ell_{11}</math><br>
<math>Some ~ u</math><br>
<math>is ~ v</math></td></tr>
<tr>
<tr>
<tr>
<tr>
<td style="border-bottom:2px solid black"><math>\texttt{Mnemonic}</math></td>
<td style="border-bottom:2px solid black"><math>\mathrm{Mnemonic}</math></td>
<td style="border-bottom:2px solid black"><math>\texttt{Category}</math></td>
<td style="border-bottom:2px solid black"><math>\mathrm{Category}</math></td>
<td style="border-bottom:2px solid black"><math>\texttt{Classical Form}</math></td>
<td style="border-bottom:2px solid black"><math>\mathrm{Classical Form}</math></td>
<td style="border-bottom:2px solid black"><math>\texttt{Alternate Form}</math></td>
<td style="border-bottom:2px solid black"><math>\mathrm{Alternate Form}</math></td>
<td style="border-bottom:2px solid black"><math>\texttt{Symmetric Form}</math></td>
<td style="border-bottom:2px solid black"><math>\mathrm{Symmetric Form}</math></td>
<td style="border-bottom:2px solid black"><math>\texttt{Operator}</math></td></tr>
<td style="border-bottom:2px solid black"><math>\mathrm{Operator}</math></td></tr>
<tr>
<tr>
<td><math>\texttt{E}</math><br><math>\texttt{Exclusive}</math></td>
<td><math>\mathrm{E}</math><br><math>\mathrm{Exclusive}</math></td>
<td><math>\texttt{Universal}</math><br><math>\texttt{Negative}</math></td>
<td><math>\mathrm{Universal}</math><br><math>\texttt{Negative}</math></td>
<td><math>\texttt{All} ~ u ~ \texttt{is} ~ \texttt{(} v \texttt{)}</math></td>
<td><math>\mathrm{All} ~ u ~ \mathrm{is} ~ \texttt{(} v \texttt{)}</math></td>
<td> </td>
<td> </td>
<td><math>\texttt{No} ~ u ~ \texttt{is} ~ v</math></td>
<td><math>\mathrm{No} ~ u ~ \mathrm{is} ~ v</math></td>
<td><math>\texttt{(} \ell_{11} \texttt{)}</math></td></tr>
<td><math>\texttt{(} \ell_{11} \texttt{)}</math></td></tr>
<tr>
<tr>
<td><math>\texttt{A}</math><br><math>\texttt{Absolute}</math></td>
<td><math>\mathrm{A}</math><br><math>\mathrm{Absolute}</math></td>
<td><math>\texttt{Universal}</math><br><math>\texttt{Affirmative}</math></td>
<td><math>\mathrm{Universal}</math><br><math>\mathrm{Affirmative}</math></td>
<td><math>\texttt{All} ~ u ~ \texttt{is} ~ v</math></td>
<td><math>\mathrm{All} ~ u ~ \mathrm{is} ~ v</math></td>
<td> </td>
<td> </td>
<td><math>\texttt{No} ~ u ~ \texttt{is} ~ \texttt{(} v \texttt{)}</math></td>
<td><math>\mathrm{No} ~ u ~ \mathrm{is} ~ \texttt{(} v \texttt{)}</math></td>
<td><math>\texttt{(} \ell_{10} \texttt{)}</math></td></tr>
<td><math>\texttt{(} \ell_{10} \texttt{)}</math></td></tr>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td><math>\texttt{All} ~ v ~ \texttt{is} ~ u</math></td>
<td><math>\mathrm{All} ~ v ~ \mathrm{is} ~ u</math></td>
<td><math>\texttt{No} ~ v ~ \texttt{is} ~ \texttt{(} u \texttt{)}</math></td>
<td><math>\mathrm{No} ~ v ~ \mathrm{is} ~ \texttt{(} u \texttt{)}</math></td>
<td><math>\texttt{No} ~ \texttt{(} u \texttt{)} ~ \texttt{is} ~ v</math></td>
<td><math>\mathrm{No} ~ \texttt{(} u \texttt{)} ~ \mathrm{is} ~ v</math></td>
<td><math>\texttt{(} \ell_{01} \texttt{)}</math></td></tr>
<td><math>\texttt{(} \ell_{01} \texttt{)}</math></td></tr>
<td style="border-bottom:2px solid black"> </td>
<td style="border-bottom:2px solid black"> </td>
<td style="border-bottom:2px solid black"> </td>
<td style="border-bottom:2px solid black"> </td>
<td style="border-bottom:2px solid black"><math>\texttt{All} ~ \texttt{(} v \texttt{)} ~ \texttt{is} ~ u</math></td>
<td style="border-bottom:2px solid black"><math>\mathrm{All} ~ \texttt{(} v \texttt{)} ~ \mathrm{is} ~ u</math></td>
<td style="border-bottom:2px solid black"><math>\texttt{No} ~ \texttt{(} v \texttt{)} ~ \texttt{is} ~ \texttt{(} u \texttt{)}</math></td>
<td style="border-bottom:2px solid black"><math>\mathrm{No} ~ \texttt{(} v \texttt{)} ~ \mathrm{is} ~ \texttt{(} u \texttt{)}</math></td>
<td style="border-bottom:2px solid black"><math>\texttt{No} ~ \texttt{(} u \texttt{)} ~ \texttt{is} ~ \texttt{(} v \texttt{)}</math></td>
<td style="border-bottom:2px solid black"><math>\mathrm{No} ~ \texttt{(} u \texttt{)} ~ \mathrm{is} ~ \texttt{(} v \texttt{)}</math></td>
<td style="border-bottom:2px solid black"><math>\texttt{(} \ell_{00} \texttt{)}</math></td></tr>
<td style="border-bottom:2px solid black"><math>\texttt{(} \ell_{00} \texttt{)}</math></td></tr>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td><math>\texttt{Some} ~ \texttt{(} u \texttt{)} ~ \texttt{is} ~ \texttt{(} v \texttt{)}</math></td>
<td><math>\mathrm{Some} ~ \texttt{(} u \texttt{)} ~ \mathrm{is} ~ \texttt{(} v \texttt{)}</math></td>
<td> </td>
<td> </td>
<td><math>\texttt{Some} ~ \texttt{(} u \texttt{)} ~ \texttt{is} ~ \texttt{(} v \texttt{)}</math></td>
<td><math>\mathrm{Some} ~ \texttt{(} u \texttt{)} ~ \mathrm{is} ~ \texttt{(} v \texttt{)}</math></td>
<td><math>\ell_{00}</math></td></tr>
<td><math>\ell_{00}</math></td></tr>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
<td><math>\texttt{Some} ~ \texttt{(} u \texttt{)} ~ \texttt{is} ~ v</math></td>
<td><math>\mathrm{Some} ~ \texttt{(} u \texttt{)} ~ \mathrm{is} ~ v</math></td>
<td> </td>
<td> </td>
<td><math>\texttt{Some} ~ \texttt{(} u \texttt{)} ~ \texttt{is} ~ v</math></td>
<td><math>\mathrm{Some} ~ \texttt{(} u \texttt{)} ~ \mathrm{is} ~ v</math></td>
<td><math>\ell_{01}</math></td></tr>
<td><math>\ell_{01}</math></td></tr>
<tr>
<tr>
<td><math>\texttt{O}</math><br><math>\texttt{Obtrusive}</math></td>
<td><math>\mathrm{O}</math><br><math>\mathrm{Obtrusive}</math></td>
<td><math>\texttt{Particular}</math><br><math>\texttt{Negative}</math></td>
<td><math>\mathrm{Particular}</math><br><math>\mathrm{Negative}</math></td>
<td><math>\texttt{Some} ~ u ~ \texttt{is} ~ \texttt{(} v \texttt{)}</math></td>
<td><math>\mathrm{Some} ~ u ~ \mathrm{is} ~ \texttt{(} v \texttt{)}</math></td>
<td> </td>
<td> </td>
<td><math>\texttt{Some} ~ u ~ \texttt{is} ~ \texttt{(} v \texttt{)}</math></td>
<td><math>\mathrm{Some} ~ u ~ \mathrm{is} ~ \texttt{(} v \texttt{)}</math></td>
<td><math>\ell_{10}</math></td></tr>
<td><math>\ell_{10}</math></td></tr>
<tr>
<tr>
<td><math>\texttt{I}</math><br><math>\texttt{Indefinite}</math></td>
<td><math>\mathrm{I}</math><br><math>\mathrm{Indefinite}</math></td>
<td><math>\texttt{Particular}</math><br><math>\texttt{Affirmative}</math></td>
<td><math>\mathrm{Particular}</math><br><math>\mathrm{Affirmative}</math></td>
<td><math>\texttt{Some} ~ u ~ \texttt{is} ~ v</math></td>
<td><math>\mathrm{Some} ~ u ~ \mathrm{is} ~ v</math></td>
<td> </td>
<td> </td>
<td><math>\texttt{Some} ~ u ~ \texttt{is} ~ v</math></td>
<td><math>\mathrm{Some} ~ u ~ \mathrm{is} ~ v</math></td>
<td><math>\ell_{11}</math></td></tr>
<td><math>\ell_{11}</math></td></tr>
</table></font>
</table>
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