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14,778 bytes added ,  19:00, 29 May 2009
→‎TeX Tables: + TeX Source
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<br>
 
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 +
===TeX Tables===
 +
 +
<pre>
 +
\tableofcontents
 +
 +
\subsection{Table A1.  Propositional Forms on Two Variables}
 +
 +
Table A1 lists equivalent expressions for the Boolean functions of two variables in a number of different notational systems.
 +
 +
\begin{quote}\begin{tabular}{|c|c|c|c|c|c|c|}
 +
\multicolumn{7}{c}{\textbf{Table A1.  Propositional Forms on Two Variables}} \\
 +
\hline
 +
$\mathcal{L}_1$ &
 +
$\mathcal{L}_2$ &&
 +
$\mathcal{L}_3$ &
 +
$\mathcal{L}_4$ &
 +
$\mathcal{L}_5$ &
 +
$\mathcal{L}_6$ \\
 +
\hline
 +
& & $x =$ & 1 1 0 0 & & & \\
 +
& & $y =$ & 1 0 1 0 & & & \\
 +
\hline
 +
$f_{0}$    &
 +
$f_{0000}$  &&
 +
0 0 0 0    &
 +
$(~)$      &
 +
$\operatorname{false}$ &
 +
$0$        \\
 +
$f_{1}$    &
 +
$f_{0001}$  &&
 +
0 0 0 1    &
 +
$(x)(y)$    &
 +
$\operatorname{neither}\ x\ \operatorname{nor}\ y$ &
 +
$\lnot x \land \lnot y$ \\
 +
$f_{2}$    &
 +
$f_{0010}$  &&
 +
0 0 1 0    &
 +
$(x)\ y$    &
 +
$y\ \operatorname{without}\ x$ &
 +
$\lnot x \land y$ \\
 +
$f_{3}$    &
 +
$f_{0011}$  &&
 +
0 0 1 1    &
 +
$(x)$      &
 +
$\operatorname{not}\ x$ &
 +
$\lnot x$  \\
 +
$f_{4}$    &
 +
$f_{0100}$  &&
 +
0 1 0 0    &
 +
$x\ (y)$    &
 +
$x\ \operatorname{without}\ y$ &
 +
$x \land \lnot y$ \\
 +
$f_{5}$    &
 +
$f_{0101}$  &&
 +
0 1 0 1    &
 +
$(y)$      &
 +
$\operatorname{not}\ y$ &
 +
$\lnot y$  \\
 +
$f_{6}$    &
 +
$f_{0110}$  &&
 +
0 1 1 0    &
 +
$(x,\ y)$  &
 +
$x\ \operatorname{not~equal~to}\ y$ &
 +
$x \ne y$  \\
 +
$f_{7}$    &
 +
$f_{0111}$  &&
 +
0 1 1 1    &
 +
$(x\ y)$    &
 +
$\operatorname{not~both}\ x\ \operatorname{and}\ y$ &
 +
$\lnot x \lor \lnot y$ \\
 +
\hline
 +
$f_{8}$    &
 +
$f_{1000}$  &&
 +
1 0 0 0    &
 +
$x\ y$      &
 +
$x\ \operatorname{and}\ y$ &
 +
$x \land y$ \\
 +
$f_{9}$    &
 +
$f_{1001}$  &&
 +
1 0 0 1    &
 +
$((x,\ y))$ &
 +
$x\ \operatorname{equal~to}\ y$ &
 +
$x = y$    \\
 +
$f_{10}$    &
 +
$f_{1010}$  &&
 +
1 0 1 0    &
 +
$y$        &
 +
$y$        &
 +
$y$        \\
 +
$f_{11}$    &
 +
$f_{1011}$  &&
 +
1 0 1 1    &
 +
$(x\ (y))$  &
 +
$\operatorname{not}\ x\ \operatorname{without}\ y$ &
 +
$x \Rightarrow y$ \\
 +
$f_{12}$    &
 +
$f_{1100}$  &&
 +
1 1 0 0    &
 +
$x$        &
 +
$x$        &
 +
$x$        \\
 +
$f_{13}$    &
 +
$f_{1101}$  &&
 +
1 1 0 1    &
 +
$((x)\ y)$  &
 +
$\operatorname{not}\ y\ \operatorname{without}\ x$ &
 +
$x \Leftarrow y$ \\
 +
$f_{14}$    &
 +
$f_{1110}$  &&
 +
1 1 1 0    &
 +
$((x)(y))$  &
 +
$x\ \operatorname{or}\ y$ &
 +
$x \lor y$  \\
 +
$f_{15}$    &
 +
$f_{1111}$  &&
 +
1 1 1 1    &
 +
$((~))$    &
 +
$\operatorname{true}$ &
 +
$1$        \\
 +
\hline
 +
\end{tabular}\end{quote}
 +
 +
\subsection{Table A2.  Propositional Forms on Two Variables}
 +
 +
Table A2 lists the sixteen Boolean functions of two variables in a different order, grouping them by structural similarity into seven natural classes.
 +
 +
\begin{quote}\begin{tabular}{|c|c|c|c|c|c|c|}
 +
\multicolumn{7}{c}{\textbf{Table A2.  Propositional Forms on Two Variables}} \\
 +
\hline
 +
$\mathcal{L}_1$ &
 +
$\mathcal{L}_2$ &&
 +
$\mathcal{L}_3$ &
 +
$\mathcal{L}_4$ &
 +
$\mathcal{L}_5$ &
 +
$\mathcal{L}_6$ \\
 +
\hline
 +
& & $x =$ & 1 1 0 0 & & & \\
 +
& & $y =$ & 1 0 1 0 & & & \\
 +
\hline
 +
$f_{0}$    &
 +
$f_{0000}$  &&
 +
0 0 0 0    &
 +
$(~)$      &
 +
$\operatorname{false}$ &
 +
$0$        \\
 +
\hline
 +
$f_{1}$    &
 +
$f_{0001}$  &&
 +
0 0 0 1    &
 +
$(x)(y)$    &
 +
$\operatorname{neither}\ x\ \operatorname{nor}\ y$ &
 +
$\lnot x \land \lnot y$ \\
 +
$f_{2}$    &
 +
$f_{0010}$  &&
 +
0 0 1 0    &
 +
$(x)\ y$    &
 +
$y\ \operatorname{without}\ x$ &
 +
$\lnot x \land y$ \\
 +
$f_{4}$    &
 +
$f_{0100}$  &&
 +
0 1 0 0    &
 +
$x\ (y)$    &
 +
$x\ \operatorname{without}\ y$ &
 +
$x \land \lnot y$ \\
 +
$f_{8}$    &
 +
$f_{1000}$  &&
 +
1 0 0 0    &
 +
$x\ y$      &
 +
$x\ \operatorname{and}\ y$ &
 +
$x \land y$ \\
 +
\hline
 +
$f_{3}$    &
 +
$f_{0011}$  &&
 +
0 0 1 1    &
 +
$(x)$      &
 +
$\operatorname{not}\ x$ &
 +
$\lnot x$  \\
 +
$f_{12}$    &
 +
$f_{1100}$  &&
 +
1 1 0 0    &
 +
$x$        &
 +
$x$        &
 +
$x$        \\
 +
\hline
 +
$f_{6}$    &
 +
$f_{0110}$  &&
 +
0 1 1 0    &
 +
$(x,\ y)$  &
 +
$x\ \operatorname{not~equal~to}\ y$ &
 +
$x \ne y$  \\
 +
$f_{9}$    &
 +
$f_{1001}$  &&
 +
1 0 0 1    &
 +
$((x,\ y))$ &
 +
$x\ \operatorname{equal~to}\ y$ &
 +
$x = y$    \\
 +
\hline
 +
$f_{5}$    &
 +
$f_{0101}$  &&
 +
0 1 0 1    &
 +
$(y)$      &
 +
$\operatorname{not}\ y$ &
 +
$\lnot y$  \\
 +
$f_{10}$    &
 +
$f_{1010}$  &&
 +
1 0 1 0    &
 +
$y$        &
 +
$y$        &
 +
$y$        \\
 +
\hline
 +
$f_{7}$    &
 +
$f_{0111}$  &&
 +
0 1 1 1    &
 +
$(x\ y)$    &
 +
$\operatorname{not~both}\ x\ \operatorname{and}\ y$ &
 +
$\lnot x \lor \lnot y$ \\
 +
$f_{11}$    &
 +
$f_{1011}$  &&
 +
1 0 1 1    &
 +
$(x\ (y))$  &
 +
$\operatorname{not}\ x\ \operatorname{without}\ y$ &
 +
$x \Rightarrow y$ \\
 +
$f_{13}$    &
 +
$f_{1101}$  &&
 +
1 1 0 1    &
 +
$((x)\ y)$  &
 +
$\operatorname{not}\ y\ \operatorname{without}\ x$ &
 +
$x \Leftarrow y$ \\
 +
$f_{14}$    &
 +
$f_{1110}$  &&
 +
1 1 1 0    &
 +
$((x)(y))$  &
 +
$x\ \operatorname{or}\ y$ &
 +
$x \lor y$  \\
 +
\hline
 +
$f_{15}$    &
 +
$f_{1111}$  &&
 +
1 1 1 1    &
 +
$((~))$    &
 +
$\operatorname{true}$ &
 +
$1$        \\
 +
\hline
 +
\end{tabular}\end{quote}
 +
 +
\subsection{Table A3.  $\operatorname{E}f$ Expanded Over Differential Features $\{ \operatorname{d}x, \operatorname{d}y \}$}
 +
 +
\begin{quote}\begin{tabular}{|c|c||c|c|c|c|}
 +
\multicolumn{6}{c}{\textbf{Table A3.  $\operatorname{E}f$ Expanded Over Differential Features $\{ \operatorname{d}x, \operatorname{d}y \}$}} \\
 +
\hline
 +
& &
 +
$\operatorname{T}_{11}$ &
 +
$\operatorname{T}_{10}$ &
 +
$\operatorname{T}_{01}$ &
 +
$\operatorname{T}_{00}$ \\
 +
& $f$ &
 +
$\operatorname{E}f|_{\operatorname{d}x\ \operatorname{d}y}$  &
 +
$\operatorname{E}f|_{\operatorname{d}x (\operatorname{d}y)}$  &
 +
$\operatorname{E}f|_{(\operatorname{d}x) \operatorname{d}y}$  &
 +
$\operatorname{E}f|_{(\operatorname{d}x)(\operatorname{d}y)}$ \\
 +
\hline
 +
$f_{0}$  & $(~)$      & $(~)$      & $(~)$      & $(~)$      & $(~)$      \\
 +
\hline
 +
$f_{1}$  & $(x)(y)$    & $x\ y$      & $x\ (y)$    & $(x)\ y$    & $(x)(y)$    \\
 +
$f_{2}$  & $(x)\ y$    & $x\ (y)$    & $x\ y$      & $(x)(y)$    & $(x)\ y$    \\
 +
$f_{4}$  & $x\ (y)$    & $(x)\ y$    & $(x)(y)$    & $x\ y$      & $x\ (y)$    \\
 +
$f_{8}$  & $x\ y$      & $(x)(y)$    & $(x)\ y$    & $x\ (y)$    & $x\ y$      \\
 +
\hline
 +
$f_{3}$  & $(x)$      & $x$        & $x$        & $(x)$      & $(x)$      \\
 +
$f_{12}$ & $x$        & $(x)$      & $(x)$      & $x$        & $x$        \\
 +
\hline
 +
$f_{6}$  & $(x,\ y)$  & $(x,\ y)$  & $((x,\ y))$ & $((x,\ y))$ & $(x,\ y)$  \\
 +
$f_{9}$  & $((x,\ y))$ & $((x,\ y))$ & $(x,\ y)$  & $(x,\ y)$  & $((x,\ y))$ \\
 +
\hline
 +
$f_{5}$  & $(y)$      & $y$        & $(y)$      & $y$        & $(y)$      \\
 +
$f_{10}$ & $y$        & $(y)$      & $y$        & $(y)$      & $y$        \\
 +
\hline
 +
$f_{7}$  & $(x\ y)$    & $((x)(y))$  & $((x)\ y)$  & $(x\ (y))$  & $(x\ y)$    \\
 +
$f_{11}$ & $(x\ (y))$  & $((x)\ y)$  & $((x)(y))$  & $(x\ y)$    & $(x\ (y))$  \\
 +
$f_{13}$ & $((x)\ y)$  & $(x\ (y))$  & $(x\ y)$    & $((x)(y))$  & $((x)\ y)$  \\
 +
$f_{14}$ & $((x)(y))$  & $(x\ y)$    & $(x\ (y))$  & $((x)\ y)$  & $((x)(y))$  \\
 +
\hline
 +
$f_{15}$ & $((~))$    & $((~))$    & $((~))$    & $((~))$    & $((~))$    \\
 +
\hline
 +
\multicolumn{2}{|c||}{\PMlinkname{Fixed Point}{FixedPoint} Total:} & 4 & 4 & 4 & 16 \\
 +
\hline
 +
\end{tabular}\end{quote}
 +
 +
\subsection{Table A4.  $\operatorname{D}f$ Expanded Over Differential Features $\{ \operatorname{d}x, \operatorname{d}y \}$}
 +
 +
\begin{quote}\begin{tabular}{|c|c||c|c|c|c|}
 +
\multicolumn{6}{c}{\textbf{Table A4.  $\operatorname{D}f$ Expanded Over Differential Features $\{ \operatorname{d}x, \operatorname{d}y \}$}} \\
 +
\hline
 +
& $f$ &
 +
$\operatorname{D}f|_{\operatorname{d}x\ \operatorname{d}y}$  &
 +
$\operatorname{D}f|_{\operatorname{d}x (\operatorname{d}y)}$  &
 +
$\operatorname{D}f|_{(\operatorname{d}x) \operatorname{d}y}$  &
 +
$\operatorname{D}f|_{(\operatorname{d}x)(\operatorname{d}y)}$ \\
 +
\hline
 +
$f_{0}$  & $(~)$      & $(~)$      & $(~)$  & $(~)$  & $(~)$ \\
 +
\hline
 +
$f_{1}$  & $(x)(y)$    & $((x,\ y))$ & $(y)$  & $(x)$  & $(~)$ \\
 +
$f_{2}$  & $(x)\ y$    & $(x,\ y)$  & $y$    & $(x)$  & $(~)$ \\
 +
$f_{4}$  & $x\ (y)$    & $(x,\ y)$  & $(y)$  & $x$    & $(~)$ \\
 +
$f_{8}$  & $x\ y$      & $((x,\ y))$ & $y$    & $x$    & $(~)$ \\
 +
\hline
 +
$f_{3}$  & $(x)$      & $((~))$    & $((~))$ & $(~)$  & $(~)$ \\
 +
$f_{12}$ & $x$        & $((~))$    & $((~))$ & $(~)$  & $(~)$ \\
 +
\hline
 +
$f_{6}$  & $(x,\ y)$  & $(~)$      & $((~))$ & $((~))$ & $(~)$ \\
 +
$f_{9}$  & $((x,\ y))$ & $(~)$      & $((~))$ & $((~))$ & $(~)$ \\
 +
\hline
 +
$f_{5}$  & $(y)$      & $((~))$    & $(~)$  & $((~))$ & $(~)$ \\
 +
$f_{10}$ & $y$        & $((~))$    & $(~)$  & $((~))$ & $(~)$ \\
 +
\hline
 +
$f_{7}$  & $(x\ y)$    & $((x,\ y))$ & $y$    & $x$    & $(~)$ \\
 +
$f_{11}$ & $(x\ (y))$  & $(x,\ y)$  & $(y)$  & $x$    & $(~)$ \\
 +
$f_{13}$ & $((x)\ y)$  & $(x,\ y)$  & $y$    & $(x)$  & $(~)$ \\
 +
$f_{14}$ & $((x)(y))$  & $((x,\ y))$ & $(y)$  & $(x)$  & $(~)$ \\
 +
\hline
 +
$f_{15}$ & $((~))$    & $(~)$      & $(~)$  & $(~)$  & $(~)$ \\
 +
\hline
 +
\end{tabular}\end{quote}
 +
 +
\subsection{Table A5.  $\operatorname{E}f$ Expanded Over Ordinary Features $\{ x, y \}$}
 +
 +
\begin{quote}\begin{tabular}{|c|c||c|c|c|c|}
 +
\multicolumn{6}{c}{\textbf{Table A5.  $\operatorname{E}f$ Expanded Over Ordinary Features $\{ x, y \}$}} \\
 +
\hline
 +
& $f$ &
 +
$\operatorname{E}f|_{x\ y}$  &
 +
$\operatorname{E}f|_{x (y)}$  &
 +
$\operatorname{E}f|_{(x) y}$  &
 +
$\operatorname{E}f|_{(x)(y)}$ \\
 +
\hline
 +
$f_{0}$ &
 +
$(~)$  &
 +
$(~)$  &
 +
$(~)$  &
 +
$(~)$  &
 +
$(~)$  \\
 +
\hline
 +
$f_{1}$  &
 +
$(x)(y)$ &
 +
$\operatorname{d}x\ \operatorname{d}y$  &
 +
$\operatorname{d}x\ (\operatorname{d}y)$ &
 +
$(\operatorname{d}x)\ \operatorname{d}y$ &
 +
$(\operatorname{d}x)(\operatorname{d}y)$ \\
 +
$f_{2}$  &
 +
$(x)\ y$ &
 +
$\operatorname{d}x\ (\operatorname{d}y)$ &
 +
$\operatorname{d}x\ \operatorname{d}y$  &
 +
$(\operatorname{d}x)(\operatorname{d}y)$ &
 +
$(\operatorname{d}x)\ \operatorname{d}y$ \\
 +
$f_{4}$  &
 +
$x\ (y)$ &
 +
$(\operatorname{d}x)\ \operatorname{d}y$ &
 +
$(\operatorname{d}x)(\operatorname{d}y)$ &
 +
$\operatorname{d}x\ \operatorname{d}y$  &
 +
$\operatorname{d}x\ (\operatorname{d}y)$ \\
 +
$f_{8}$ &
 +
$x\ y$  &
 +
$(\operatorname{d}x)(\operatorname{d}y)$ &
 +
$(\operatorname{d}x)\ \operatorname{d}y$ &
 +
$\operatorname{d}x\ (\operatorname{d}y)$ &
 +
$\operatorname{d}x\ \operatorname{d}y$  \\
 +
\hline
 +
$f_{3}$ &
 +
$(x)$  &
 +
$\operatorname{d}x$  &
 +
$\operatorname{d}x$  &
 +
$(\operatorname{d}x)$ &
 +
$(\operatorname{d}x)$ \\
 +
$f_{12}$ &
 +
$x$      &
 +
$(\operatorname{d}x)$ &
 +
$(\operatorname{d}x)$ &
 +
$\operatorname{d}x$  &
 +
$\operatorname{d}x$  \\
 +
\hline
 +
$f_{6}$  &
 +
$(x,\ y)$ &
 +
$(\operatorname{d}x,\ \operatorname{d}y)$  &
 +
$((\operatorname{d}x,\ \operatorname{d}y))$ &
 +
$((\operatorname{d}x,\ \operatorname{d}y))$ &
 +
$(\operatorname{d}x,\ \operatorname{d}y)$  \\
 +
$f_{9}$    &
 +
$((x,\ y))$ &
 +
$((\operatorname{d}x,\ \operatorname{d}y))$ &
 +
$(\operatorname{d}x,\ \operatorname{d}y)$  &
 +
$(\operatorname{d}x,\ \operatorname{d}y)$  &
 +
$((\operatorname{d}x,\ \operatorname{d}y))$ \\
 +
\hline
 +
$f_{5}$ &
 +
$(y)$  &
 +
$\operatorname{d}y$  &
 +
$(\operatorname{d}y)$ &
 +
$\operatorname{d}y$  &
 +
$(\operatorname{d}y)$ \\
 +
$f_{10}$ &
 +
$y$      &
 +
$(\operatorname{d}y)$ &
 +
$\operatorname{d}y$  &
 +
$(\operatorname{d}y)$ &
 +
$\operatorname{d}y$  \\
 +
\hline
 +
$f_{7}$  &
 +
$(x\ y)$ &
 +
$((\operatorname{d}x)(\operatorname{d}y))$ &
 +
$((\operatorname{d}x)\ \operatorname{d}y)$ &
 +
$(\operatorname{d}x\ (\operatorname{d}y))$ &
 +
$(\operatorname{d}x\ \operatorname{d}y)$  \\
 +
$f_{11}$  &
 +
$(x\ (y))$ &
 +
$((\operatorname{d}x)\ \operatorname{d}y)$ &
 +
$((\operatorname{d}x)(\operatorname{d}y))$ &
 +
$(\operatorname{d}x\ \operatorname{d}y)$  &
 +
$(\operatorname{d}x\ (\operatorname{d}y))$ \\
 +
$f_{13}$  &
 +
$((x)\ y)$ &
 +
$(\operatorname{d}x\ (\operatorname{d}y))$ &
 +
$(\operatorname{d}x\ \operatorname{d}y)$  &
 +
$((\operatorname{d}x)(\operatorname{d}y))$ &
 +
$((\operatorname{d}x)\ \operatorname{d}y)$ \\
 +
$f_{14}$  &
 +
$((x)(y))$ &
 +
$(\operatorname{d}x\ \operatorname{d}y)$  &
 +
$(\operatorname{d}x\ (\operatorname{d}y))$ &
 +
$((\operatorname{d}x)\ \operatorname{d}y)$ &
 +
$((\operatorname{d}x)(\operatorname{d}y))$ \\
 +
\hline
 +
$f_{15}$ &
 +
$((~))$  &
 +
$((~))$  &
 +
$((~))$  &
 +
$((~))$  &
 +
$((~))$  \\
 +
\hline
 +
\end{tabular}\end{quote}
 +
 +
\subsection{Table A6.  $\operatorname{D}f$ Expanded Over Ordinary Features $\{ x, y \}$}
 +
 +
\begin{quote}\begin{tabular}{|c|c||c|c|c|c|}
 +
\multicolumn{6}{c}{\textbf{Table A6.  $\operatorname{D}f$ Expanded Over Ordinary Features $\{ x, y \}$}} \\
 +
\hline
 +
& $f$ &
 +
$\operatorname{D}f|_{x\ y}$  &
 +
$\operatorname{D}f|_{x (y)}$  &
 +
$\operatorname{D}f|_{(x) y}$  &
 +
$\operatorname{D}f|_{(x)(y)}$ \\
 +
\hline
 +
$f_{0}$ &
 +
$(~)$  &
 +
$(~)$  &
 +
$(~)$  &
 +
$(~)$  &
 +
$(~)$  \\
 +
\hline
 +
$f_{1}$  &
 +
$(x)(y)$ &
 +
$\operatorname{d}x\ \operatorname{d}y$    &
 +
$\operatorname{d}x\ (\operatorname{d}y)$  &
 +
$(\operatorname{d}x)\ \operatorname{d}y$  &
 +
$((\operatorname{d}x)(\operatorname{d}y))$ \\
 +
$f_{2}$  &
 +
$(x)\ y$ &
 +
$\operatorname{d}x\ (\operatorname{d}y)$  &
 +
$\operatorname{d}x\ \operatorname{d}y$    &
 +
$((\operatorname{d}x)(\operatorname{d}y))$ &
 +
$(\operatorname{d}x)\ \operatorname{d}y$  \\
 +
$f_{4}$  &
 +
$x\ (y)$ &
 +
$(\operatorname{d}x)\ \operatorname{d}y$  &
 +
$((\operatorname{d}x)(\operatorname{d}y))$ &
 +
$\operatorname{d}x\ \operatorname{d}y$    &
 +
$\operatorname{d}x\ (\operatorname{d}y)$  \\
 +
$f_{8}$ &
 +
$x\ y$  &
 +
$((\operatorname{d}x)(\operatorname{d}y))$ &
 +
$(\operatorname{d}x)\ \operatorname{d}y$  &
 +
$\operatorname{d}x\ (\operatorname{d}y)$  &
 +
$\operatorname{d}x\ \operatorname{d}y$    \\
 +
\hline
 +
$f_{3}$ &
 +
$(x)$  &
 +
$\operatorname{d}x$ &
 +
$\operatorname{d}x$ &
 +
$\operatorname{d}x$ &
 +
$\operatorname{d}x$ \\
 +
$f_{12}$ &
 +
$x$      &
 +
$\operatorname{d}x$ &
 +
$\operatorname{d}x$ &
 +
$\operatorname{d}x$ &
 +
$\operatorname{d}x$ \\
 +
\hline
 +
$f_{6}$  &
 +
$(x,\ y)$ &
 +
$(\operatorname{d}x,\ \operatorname{d}y)$ &
 +
$(\operatorname{d}x,\ \operatorname{d}y)$ &
 +
$(\operatorname{d}x,\ \operatorname{d}y)$ &
 +
$(\operatorname{d}x,\ \operatorname{d}y)$ \\
 +
$f_{9}$    &
 +
$((x,\ y))$ &
 +
$(\operatorname{d}x,\ \operatorname{d}y)$ &
 +
$(\operatorname{d}x,\ \operatorname{d}y)$ &
 +
$(\operatorname{d}x,\ \operatorname{d}y)$ &
 +
$(\operatorname{d}x,\ \operatorname{d}y)$ \\
 +
\hline
 +
$f_{5}$ &
 +
$(y)$  &
 +
$\operatorname{d}y$ &
 +
$\operatorname{d}y$ &
 +
$\operatorname{d}y$ &
 +
$\operatorname{d}y$ \\
 +
$f_{10}$ &
 +
$y$      &
 +
$\operatorname{d}y$ &
 +
$\operatorname{d}y$ &
 +
$\operatorname{d}y$ &
 +
$\operatorname{d}y$ \\
 +
\hline
 +
$f_{7}$  &
 +
$(x\ y)$ &
 +
$((\operatorname{d}x)(\operatorname{d}y))$ &
 +
$(\operatorname{d}x)\ \operatorname{d}y$  &
 +
$\operatorname{d}x\ (\operatorname{d}y)$  &
 +
$\operatorname{d}x\ \operatorname{d}y$    \\
 +
$f_{11}$  &
 +
$(x\ (y))$ &
 +
$(\operatorname{d}x)\ \operatorname{d}y$  &
 +
$((\operatorname{d}x)(\operatorname{d}y))$ &
 +
$\operatorname{d}x\ \operatorname{d}y$    &
 +
$\operatorname{d}x\ (\operatorname{d}y)$  \\
 +
$f_{13}$  &
 +
$((x)\ y)$ &
 +
$\operatorname{d}x\ (\operatorname{d}y)$  &
 +
$\operatorname{d}x\ \operatorname{d}y$    &
 +
$((\operatorname{d}x)(\operatorname{d}y))$ &
 +
$(\operatorname{d}x)\ \operatorname{d}y$  \\
 +
$f_{14}$  &
 +
$((x)(y))$ &
 +
$\operatorname{d}x\ \operatorname{d}y$    &
 +
$\operatorname{d}x\ (\operatorname{d}y)$  &
 +
$(\operatorname{d}x)\ \operatorname{d}y$  &
 +
$((\operatorname{d}x)(\operatorname{d}y))$ \\
 +
\hline
 +
$f_{15}$ &
 +
$((~))$  &
 +
$(~)$    &
 +
$(~)$    &
 +
$(~)$    &
 +
$(~)$    \\
 +
\hline
 +
\end{tabular}\end{quote}
 +
</pre>
    
==Inquiry Driven Systems==
 
==Inquiry Driven Systems==
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