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Relation Theory

Six Ways of Looking at a Triadic Relation

LaTeX

A ~\mathrm{gives}~ B ~\mathrm{to}~ C

\begin{array}{lll}  A ~\mathrm{gives}~ B ~\mathrm{to}~ C  & \qquad &  A ~\mathrm{benefits}~ C ~\mathrm{with}~ B  \\  B ~\mathrm{enriches}~ C ~\mathrm{at~expense~of}~ A  & \qquad &  C ~\mathrm{receives}~ B ~\mathrm{from}~ A  \\  C ~\mathrm{thanks}~ A ~\mathrm{for}~ B  & \qquad &  B ~\mathrm{leaves}~ A ~\mathrm{for}~ C  \end{array}

PNG

Six Ways of Looking at a Triadic Relation

Truth Tables

Self-Dual Logical Graphs

LaTeX

\begin{array}{|c|c||c|c|c|c|}  \multicolumn{6}{c}{\text{Self-Dual Logical Graphs}} \\[2pt]  \hline  x & y & f_{12} & f_{10} & f_{3}                 & f_{5} \\  ~ & ~ & x      & y      & \texttt{(}x\texttt{)} & \texttt{(}y\texttt{)} \\  \hline\hline  0 & 0 & 0 & 0 & 1 & 1 \\  0 & 1 & 0 & 1 & 1 & 0 \\  1 & 0 & 1 & 0 & 0 & 1 \\  1 & 1 & 1 & 1 & 0 & 0 \\  \hline  \end{array}

PNG

Self-Dual Logical Graphs

Constants and Amphecks

LaTeX

\begin{array}{|c|c||c|c||c|c|}  \multicolumn{6}{c}{\text{Constants and Amphecks}} \\[2pt]  \hline  x & y & f_{15} & f_{0} & f_{7} & f_{1} \\  \hline\hline  0 & 0 & 1 & 0 & 1 & 1 \\  0 & 1 & 1 & 0 & 1 & 0 \\  1 & 0 & 1 & 0 & 1 & 0 \\  1 & 1 & 1 & 0 & 0 & 0 \\  \hline\hline  \multicolumn{2}{|c||}{\text{Ex}}   & ~ & ~ \texttt{( )} ~ & \texttt{(} xy \texttt{)} & \texttt{(} x \texttt{)(} y \texttt{)} \\  \multicolumn{2}{|c||}{\text{En}}   & ~ \texttt{( )} ~ & ~ & \texttt{(} x \texttt{)(} y \texttt{)} & \texttt{(} xy \texttt{)} \\  \hline  \end{array}

PNG

Constants and Amphecks