Work 9

Difference Map • Conjunction PQR

Version 1 (a)

\begin{array}{*{4}{l}}  \multicolumn{4}{l}{\mathrm{D}f(p, q, r, \mathrm{d}p, \mathrm{d}q, \mathrm{d}r) =}  \\[10pt]  &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~}  & + &  \texttt{~} p \texttt{~~} q \texttt{~(} r \texttt{)} \cdot  \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  & + &  \texttt{~} p \texttt{~(} q \texttt{)~} r \texttt{~} \cdot  \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  & + &  \texttt{~} p \texttt{~(} q \texttt{)(} r \texttt{)} \cdot  \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  \end{array}
 
\begin{array}{*{4}{l}}  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)}  & + &  \texttt{(} p \texttt{)~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~}  & + &  \texttt{(} p \texttt{)~} q \texttt{~(} r \texttt{)} \cdot  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  & + &  \texttt{(} p \texttt{)(} q \texttt{)~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  & + &  \texttt{(} p \texttt{)(} q \texttt{)(} r \texttt{)} \cdot  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  \end{array}

Version 1 (b)

\begin{array}{*{4}{l}}  \multicolumn{4}{l}{\mathrm{D}f(p, q, r, \mathrm{d}p, \mathrm{d}q, \mathrm{d}r) =}  \\[10pt]  &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  & + &  \texttt{(} p \texttt{)(} q \texttt{)(} r \texttt{)} \cdot  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  & + &  \texttt{(} p \texttt{)(} q \texttt{)~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~}  & + &  \texttt{(} p \texttt{)~} q \texttt{~(} r \texttt{)} \cdot  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~}  \end{array}
 
\begin{array}{*{4}{l}}  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)}  & + &  \texttt{(} p \texttt{)~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  & + &  \texttt{~} p \texttt{~(} q \texttt{)(} r \texttt{)} \cdot  \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  & + &  \texttt{~} p \texttt{~(} q \texttt{)~} r \texttt{~} \cdot  \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~}  & + &  \texttt{~} p \texttt{~~} q \texttt{~(} r \texttt{)} \cdot  \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~}\end{array}

Version 4

\begin{array}{*{4}{l}}  \multicolumn{4}{l}{\mathrm{D}f(p, q, r, \mathrm{d}p, \mathrm{d}q, \mathrm{d}r) =}  \\[10pt]  &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)}  & + &  \texttt{(} p \texttt{)~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  & + &  \texttt{~} p \texttt{~(} q \texttt{)~} r \texttt{~} \cdot  \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~}  & + &  \texttt{~} p \texttt{~~} q \texttt{~(} r \texttt{)} \cdot  \texttt{(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~}  \end{array}
 
\begin{array}{*{4}{l}}  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  & + &  \texttt{(} p \texttt{)(} q \texttt{)~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~}  & + &  \texttt{(} p \texttt{)~} q \texttt{~(} r \texttt{)} \cdot  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  & + &  \texttt{~} p \texttt{~(} q \texttt{)(} r \texttt{)} \cdot  \texttt{(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  \\[10pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~} \cdot  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  & + &  \texttt{(} p \texttt{)(} q \texttt{)(} r \texttt{)} \cdot  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  \end{array}

Column Sum

\begin{array}{*{4}{c}}  \multicolumn{4}{l}{\mathrm{D}f(p, q, r, \mathrm{d}p, \mathrm{d}q, \mathrm{d}r) =}  \\[10pt]  &  \texttt{~} p \texttt{~~} q \texttt{~~} r \texttt{~}  & \cdot &  \texttt{((} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{))}  \\[4pt]  + &  \texttt{(} p \texttt{)~} q \texttt{~~} r \texttt{~}  & \cdot &  \texttt{~~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)~}  \\[4pt]  + &  \texttt{~} p \texttt{~(} q \texttt{)~} r \texttt{~}  & \cdot &  \texttt{~(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)~}  \\[4pt]  + &  \texttt{~} p \texttt{~~} q \texttt{~(} r \texttt{)}  & \cdot &  \texttt{~(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~~}  \\[4pt]  + &  \texttt{(} p \texttt{)(} q \texttt{)~} r \texttt{~}  & \cdot &  \texttt{~~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)~}  \\[4pt]  + &  \texttt{(} p \texttt{)~} q \texttt{~(} r \texttt{)}  & \cdot &  \texttt{~~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)~} \mathrm{d}r \texttt{~~}  \\[4pt]  + &  \texttt{~} p \texttt{~(} q \texttt{)(} r \texttt{)}  & \cdot &  \texttt{~(} \mathrm{d}p \texttt{)~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~~}  \\[4pt]  + &  \texttt{(} p \texttt{)(} q \texttt{)(} r \texttt{)}  & \cdot &  \texttt{~~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~~}  \end{array}

Row Sum

Version 1

\begin{array}{*{4}{c}}  \multicolumn{4}{l}{\mathrm{D}f(p, q, r, \mathrm{d}p, \mathrm{d}q, \mathrm{d}r) =}  \\[10pt]  &  p \texttt{~} q \texttt{~} r  & \cdot &  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  \\[4pt]  + &  p \texttt{~} q  & \cdot &  \texttt{~} \mathrm{d}r \texttt{~(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)}  \\[4pt]  + &  p \texttt{~} r  & \cdot &  \texttt{~} \mathrm{d}q \texttt{~(} \mathrm{d}p \texttt{)(} \mathrm{d}r \texttt{)}  \\[4pt]  + &  q \texttt{~} r  & \cdot &  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)}  \\[4pt]  + &  \texttt{((} p \texttt{,} q \texttt{))} ~ r  & \cdot &  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  \\[4pt]  + &  \texttt{((} p \texttt{,} r \texttt{))} ~ q  & \cdot &  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}r \texttt{~(} \mathrm{d}q \texttt{)}  \\[4pt]  + &  \texttt{((} q \texttt{,} r \texttt{))} ~ p  & \cdot &  \texttt{~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~(} \mathrm{d}p \texttt{)}  \\[4pt]  + &  \texttt{(} p \texttt{)(} q \texttt{)(} r \texttt{)}  & \cdot &  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  \end{array}

Version 2

\begin{array}{*{4}{c}}  \multicolumn{4}{l}{\mathrm{D}f(p, q, r, \mathrm{d}p, \mathrm{d}q, \mathrm{d}r) =}  \\[10pt]  &  \texttt{~} \mathrm{d}p \texttt{~(} \mathrm{d}q \texttt{)(} \mathrm{d}r \texttt{)}  & \cdot &  q \texttt{~} r  \\[4pt]  + &  \texttt{~} \mathrm{d}q \texttt{~(} \mathrm{d}p \texttt{)(} \mathrm{d}r \texttt{)}  & \cdot &  p \texttt{~} r  \\[4pt]  + &  \texttt{~} \mathrm{d}r \texttt{~(} \mathrm{d}p \texttt{)(} \mathrm{d}q \texttt{)}  & \cdot &  p \texttt{~} q  \\[4pt]  + &  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~(} \mathrm{d}r \texttt{)}  & \cdot &  \texttt{((} p \texttt{,} q \texttt{))} ~ r  \\[4pt]  + &  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}r \texttt{~(} \mathrm{d}q \texttt{)}  & \cdot &  \texttt{((} p \texttt{,} r \texttt{))} ~ q  \\[4pt]  + &  \texttt{~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~(} \mathrm{d}p \texttt{)}  & \cdot &  \texttt{((} q \texttt{,} r \texttt{))} ~ p  \\[4pt]  + &  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  & \cdot &  p \texttt{~} q \texttt{~} r  \\[4pt]  + &  \texttt{~} \mathrm{d}p \texttt{~~} \mathrm{d}q \texttt{~~} \mathrm{d}r \texttt{~}  & \cdot &  \texttt{(} p \texttt{)(} q \texttt{)(} r \texttt{)}  \end{array}

Differential Logic Tables • Conjunction PQR

Summary Tables

LaTeX Tables

\begin{array}{|*{8}{c}|}  \multicolumn{8}{c}{\text{Difference Map}~\text{D}(pqr)}  \\[4pt]  \hline&&&&&&&  \\  \texttt{~}p\texttt{~~}q\texttt{~~}r\texttt{~}&  \texttt{(}p\texttt{)~}q\texttt{~~}r\texttt{~}&  \texttt{~}p\texttt{~(}q\texttt{)~}r\texttt{~}&  \texttt{~}p\texttt{~~}q\texttt{~(}r\texttt{)}&  \texttt{(}p\texttt{)(}q\texttt{)~}r\texttt{~}&  \texttt{(}p\texttt{)~}q\texttt{~(}r\texttt{)}&  \texttt{~}p\texttt{~(}q\texttt{)(}r\texttt{)}&  \texttt{(}p\texttt{)(}q\texttt{)(}r\texttt{)}  \\[8pt]  \hline&&&&&&&  \\  0&&&&&&&  \\  \texttt{~}\text{d}p\texttt{~(}\text{d}q\texttt{)(}\text{d}r\texttt{)}&  \text{d}p\texttt{(}\text{d}q\texttt{)(}\text{d}r\texttt{)}&&&&&&  \\  \texttt{(}\text{d}p\texttt{)~}\text{d}q\texttt{~(}\text{d}r\texttt{)}&&  \texttt{(}\text{d}p\texttt{)}\text{d}q\texttt{(}\text{d}r\texttt{)}&&&&&  \\  \texttt{(}\text{d}p\texttt{)(}\text{d}q\texttt{)~}\text{d}r\texttt{~}&&&  \texttt{(}\text{d}p\texttt{)(}\text{d}q\texttt{)}\text{d}r&&&&  \\  \texttt{~}\text{d}p\texttt{~~}\text{d}q\texttt{~(}\text{d}r\texttt{)}&&&&  \text{d}p~\text{d}q\texttt{(}\text{d}r\texttt{)}&&&  \\  \texttt{~}\text{d}p\texttt{~(}\text{d}q\texttt{)~}\text{d}r\texttt{~}&&&&&  \text{d}p\texttt{(}\text{d}q\texttt{)}\text{d}r&&  \\  \texttt{(}\text{d}p\texttt{)~}\text{d}q\texttt{~~}\text{d}r\texttt{~}&&&&&&  \texttt{(}\text{d}p\texttt{)}\text{d}q~\text{d}r&  \\  \texttt{~}\text{d}p\texttt{~~}\text{d}q\texttt{~~}\text{d}r\texttt{~}&&&&&&&  \text{d}p~\text{d}q~\text{d}r  \\[8pt]  \hline&&&&&&&  \\  \texttt{((}\text{d}p\texttt{)(}\text{d}q\texttt{)(}\text{d}r\texttt{))}&  \text{d}p\texttt{(}\text{d}q\texttt{)(}\text{d}r\texttt{)}&  \texttt{(}\text{d}p\texttt{)}\text{d}q\texttt{(}\text{d}r\texttt{)}&  \texttt{(}\text{d}p\texttt{)(}\text{d}q\texttt{)}\text{d}r&  \text{d}p~\text{d}q\texttt{(}\text{d}r\texttt{)}&  \text{d}p\texttt{(}\text{d}q\texttt{)}\text{d}r&  \texttt{(}\text{d}p\texttt{)}\text{d}q~\text{d}r&  \text{d}p~\text{d}q~\text{d}r  \\[8pt]  \hline  \end{array}

PNG Images

Table 4.0 PQR Difference Map Col Sum

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