User:Jon Awbrey/TEST
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The following Tables develop these ideas in more detail.
| \(\begin{matrix}u\!:\\v\!:\end{matrix}\) | \(\begin{matrix}1100\\1010\end{matrix}\) | \(f\) | \(\begin{smallmatrix} \texttt{(} \ell_{11} \texttt{)} \\ \mathrm{No} ~ u \\ \mathrm{is} ~ v \end{smallmatrix}\) | \(\begin{smallmatrix} \texttt{(} \ell_{10} \texttt{)} \\ \mathrm{No} ~ u \\ \mathrm{is} ~ \texttt{(} v \texttt{)} \end{smallmatrix}\) | \(\begin{smallmatrix} \texttt{(} \ell_{01} \texttt{)} \\ \mathrm{No} ~ \texttt{(} u \texttt{)} \\ \mathrm{is} ~ v \end{smallmatrix}\) | \(\begin{smallmatrix} \texttt{(} \ell_{00} \texttt{)} \\ \mathrm{No} ~ \texttt{(} u \texttt{)} \\ \mathrm{is} ~ \texttt{(} v \texttt{)} \end{smallmatrix}\) | \(\begin{smallmatrix} \ell_{00} \\ \mathrm{Some} ~ \texttt{(} u \texttt{)} \\ \mathrm{is} ~ \texttt{(} v \texttt{)} \end{smallmatrix}\) | \(\begin{smallmatrix} \ell_{01} \\ \mathrm{Some} ~ \texttt{(} u \texttt{)} \\ \mathrm{is} ~ v \end{smallmatrix}\) | \(\begin{smallmatrix} \ell_{10} \\ \mathrm{Some} ~ u \\ \mathrm{is} ~ \texttt{(} v \texttt{)} \end{smallmatrix}\) | \(\begin{smallmatrix} \ell_{11} \\ \mathrm{Some} ~ u \\ \mathrm{is} ~ v \end{smallmatrix}\) |
| \(f_{0}\) | \(0000\) | \(\texttt{(~)}\) | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
| \(f_{1}\) | \(0001\) | \(\texttt{(} u \texttt{)(} v \texttt{)}\) | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 |
| \(f_{2}\) | \(0010\) | \(\texttt{(} u\texttt{)} ~ v\) | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 |
| \(f_{3}\) | \(0011\) | \(\texttt{(} u \texttt{)}\) | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 |
| \(f_{4}\) | \(0100\) | \(u ~ \texttt{(} v \texttt{)}\) | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 |
| \(f_{5}\) | \(0101\) | \(\texttt{(} v \texttt{)}\) | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
| \(f_{6}\) | \(0110\) | \(\texttt{(} u \texttt{,} v \texttt{)}\) | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 |
| \(f_{7}\) | \(0111\) | \(\texttt{(} u ~ v \texttt{)}\) | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 |
| \(f_{8}\) | \(1000\) | \(u ~ v\) | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 |
| \(f_{9}\) | \(1001\) | \(\texttt{((} u \texttt{,} v \texttt{))}\) | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 |
| \(f_{10}\) | \(1010\) | \(v\) | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |
| \(f_{11}\) | \(1011\) | \(\texttt{(} u ~ \texttt{(} v \texttt{))}\) | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 |
| \(f_{12}\) | \(1100\) | \(u\) | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 |
| \(f_{13}\) | \(1101\) | \(\texttt{((} u \texttt{)} ~ v \texttt{)}\) | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 |
| \(f_{14}\) | \(1110\) | \(\texttt{((} u \texttt{)(} v \texttt{))}\) | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 |
| \(f_{15}\) | \(1111\) | \(\texttt{((~))}\) | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
| \(\begin{matrix}u\!:\\v\!:\end{matrix}\) | \(\begin{matrix}1100\\1010\end{matrix}\) | \(f\) | \(\begin{smallmatrix} \texttt{(} \ell_{11} \texttt{)} \\ \mathrm{No} ~ u \\ \mathrm{is} ~ v \end{smallmatrix}\) | \(\begin{smallmatrix} \texttt{(} \ell_{10} \texttt{)} \\ \mathrm{No} ~ u \\ \mathrm{is} ~ \texttt{(} v \texttt{)} \end{smallmatrix}\) | \(\begin{smallmatrix} \texttt{(} \ell_{01} \texttt{)} \\ \mathrm{No} ~ \texttt{(} u \texttt{)} \\ \mathrm{is} ~ v \end{smallmatrix}\) | \(\begin{smallmatrix} \texttt{(} \ell_{00} \texttt{)} \\ \mathrm{No} ~ \texttt{(} u \texttt{)} \\ \mathrm{is} ~ \texttt{(} v \texttt{)} \end{smallmatrix}\) | \(\begin{smallmatrix} \ell_{00} \\ \mathrm{Some} ~ \texttt{(} u \texttt{)} \\ \mathrm{is} ~ \texttt{(} v \texttt{)} \end{smallmatrix}\) | \(\begin{smallmatrix} \ell_{01} \\ \mathrm{Some} ~ \texttt{(} u \texttt{)} \\ \mathrm{is} ~ v \end{smallmatrix}\) | \(\begin{smallmatrix} \ell_{10} \\ \mathrm{Some} ~ u \\ \mathrm{is} ~ \texttt{(} v \texttt{)} \end{smallmatrix}\) | \(\begin{smallmatrix} \ell_{11} \\ \mathrm{Some} ~ u \\ \mathrm{is} ~ v \end{smallmatrix}\) |
| \(f_{0}\) | \(0000\) | \(\texttt{(~)}\) | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
| \(f_{1}\) | \(0001\) | \(\texttt{(} u \texttt{)(} v \texttt{)}\) | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 |
| \(f_{2}\) | \(0010\) | \(\texttt{(} u\texttt{)} ~ v\) | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 |
| \(f_{4}\) | \(0100\) | \(u ~ \texttt{(} v \texttt{)}\) | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 |
| \(f_{8}\) | \(1000\) | \(u ~ v\) | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 |
| \(f_{3}\) | \(0011\) | \(\texttt{(} u \texttt{)}\) | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 |
| \(f_{12}\) | \(1100\) | \(u\) | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 |
| \(f_{6}\) | \(0110\) | \(\texttt{(} u \texttt{,} v \texttt{)}\) | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 |
| \(f_{9}\) | \(1001\) | \(\texttt{((} u \texttt{,} v \texttt{))}\) | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 |
| \(f_{5}\) | \(0101\) | \(\texttt{(} v \texttt{)}\) | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
| \(f_{10}\) | \(1010\) | \(v\) | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |
| \(f_{7}\) | \(0111\) | \(\texttt{(} u ~ v \texttt{)}\) | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 |
| \(f_{11}\) | \(1011\) | \(\texttt{(} u ~ \texttt{(} v \texttt{))}\) | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 |
| \(f_{13}\) | \(1101\) | \(\texttt{((} u \texttt{)} ~ v \texttt{)}\) | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 |
| \(f_{14}\) | \(1110\) | \(\texttt{((} u \texttt{)(} v \texttt{))}\) | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 |
| \(f_{15}\) | \(1111\) | \(\texttt{((~))}\) | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
| \(\mathrm{Mnemonic}\) | \(\mathrm{Category}\) | \(\mathrm{Classical~Form}\) | \(\mathrm{Alternate~Form}\) | \(\mathrm{Symmetric~Form}\) | \(\mathrm{Operator}\) |
| \(\mathrm{E}\) \(\mathrm{Exclusive}\) |
\(\mathrm{Universal}\) \(\mathrm{Negative}\) |
\(\mathrm{All} ~ u ~ \mathrm{is} ~ \texttt{(} v \texttt{)}\) | \(\mathrm{No} ~ u ~ \mathrm{is} ~ v\) | \(\texttt{(} \ell_{11} \texttt{)}\) | |
| \(\mathrm{A}\) \(\mathrm{Absolute}\) |
\(\mathrm{Universal}\) \(\mathrm{Affirmative}\) |
\(\mathrm{All} ~ u ~ \mathrm{is} ~ v\) | \(\mathrm{No} ~ u ~ \mathrm{is} ~ \texttt{(} v \texttt{)}\) | \(\texttt{(} \ell_{10} \texttt{)}\) | |
| \(\mathrm{All} ~ v ~ \mathrm{is} ~ u\) | \(\mathrm{No} ~ v ~ \mathrm{is} ~ \texttt{(} u \texttt{)}\) | \(\mathrm{No} ~ \texttt{(} u \texttt{)} ~ \mathrm{is} ~ v\) | \(\texttt{(} \ell_{01} \texttt{)}\) | ||
| \(\mathrm{All} ~ \texttt{(} v \texttt{)} ~ \mathrm{is} ~ u\) | \(\mathrm{No} ~ \texttt{(} v \texttt{)} ~ \mathrm{is} ~ \texttt{(} u \texttt{)}\) | \(\mathrm{No} ~ \texttt{(} u \texttt{)} ~ \mathrm{is} ~ \texttt{(} v \texttt{)}\) | \(\texttt{(} \ell_{00} \texttt{)}\) | ||
| \(\mathrm{Some} ~ \texttt{(} u \texttt{)} ~ \mathrm{is} ~ \texttt{(} v \texttt{)}\) | \(\mathrm{Some} ~ \texttt{(} u \texttt{)} ~ \mathrm{is} ~ \texttt{(} v \texttt{)}\) | \(\ell_{00}\) | |||
| \(\mathrm{Some} ~ \texttt{(} u \texttt{)} ~ \mathrm{is} ~ v\) | \(\mathrm{Some} ~ \texttt{(} u \texttt{)} ~ \mathrm{is} ~ v\) | \(\ell_{01}\) | |||
| \(\mathrm{O}\) \(\mathrm{Obtrusive}\) |
\(\mathrm{Particular}\) \(\mathrm{Negative}\) |
\(\mathrm{Some} ~ u ~ \mathrm{is} ~ \texttt{(} v \texttt{)}\) | \(\mathrm{Some} ~ u ~ \mathrm{is} ~ \texttt{(} v \texttt{)}\) | \(\ell_{10}\) | |
| \(\mathrm{I}\) \(\mathrm{Indefinite}\) |
\(\mathrm{Particular}\) \(\mathrm{Affirmative}\) |
\(\mathrm{Some} ~ u ~ \mathrm{is} ~ v\) | \(\mathrm{Some} ~ u ~ \mathrm{is} ~ v\) | \(\ell_{11}\) |
