12,080
edits
Changes
MyWikiBiz, Author Your Legacy — Friday January 10, 2025
Jump to navigationJump to searchDirectory talk:Jon Awbrey/Papers/Differential Propositional Calculus (view source)
Revision as of 04:34, 7 June 2008
, 04:34, 7 June 2008→Appendices @ PlanetMath : TeX Format: copy tables from planet math
=Appendices @ PlanetMath : TeX Format=
=Appendices @ PlanetMath : TeX Format=
==Table 1==
<pre>
\begin{quote}\begin{tabular}{|c|c|c|c|c|c|c|}
\multicolumn{7}{c}{Table 1. 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 & $(~)$ & false & $0$ \\
$f_{1}$ & $f_{0001}$ & & 0 0 0 1 & $(x)(y)$ & neither $x$ nor $y$ & $\lnot x \land \lnot y $ \\
$f_{2}$ & $f_{0010}$ & & 0 0 1 0 & $(x)\ y$ & $y$ and not $x$ & $\lnot x \land y$ \\
$f_{3}$ & $f_{0011}$ & & 0 0 1 1 & $(x)$ & not $x$ & $\lnot x$ \\
$f_{4}$ & $f_{0100}$ & & 0 1 0 0 & $x\ (y)$ & $x$ and not $y$ & $x \land \lnot y$ \\
$f_{5}$ & $f_{0101}$ & & 0 1 0 1 & $(y)$ & not $y$ & $\lnot y$ \\
$f_{6}$ & $f_{0110}$ & & 0 1 1 0 & $(x,\ y)$ & $x$ not equal to $y$ & $x \ne y$ \\
$f_{7}$ & $f_{0111}$ & & 0 1 1 1 & $(x\ y)$ & not both $x$ and $y$ & $\lnot x \lor \lnot y$ \\
\hline
$f_{8}$ & $f_{1000}$ & & 1 0 0 0 & $x\ y$ & $x$ and $y$ & $x \land y$ \\
$f_{9}$ & $f_{1001}$ & & 1 0 0 1 & $((x,\ y))$ & $x$ equal to $y$ & $x = y$ \\
$f_{10}$ & $f_{1010}$ & & 1 0 1 0 & $y$ & $y$ & $y$ \\
$f_{11}$ & $f_{1011}$ & & 1 0 1 1 & $(x\ (y))$ & not $x$ without $y$ & $x \Rightarrow y$ \\
$f_{12}$ & $f_{1100}$ & & 1 1 0 0 & $x$ & $x$ & $x$ \\
$f_{13}$ & $f_{1101}$ & & 1 1 0 1 & $((x)\ y)$ & not $y$ without $x$ & $x \Leftarrow y$ \\
$f_{14}$ & $f_{1110}$ & & 1 1 1 0 & $((x)(y))$ & $x$ or $y$ & $x \lor y$ \\
$f_{15}$ & $f_{1111}$ & & 1 1 1 1 & $((~))$ & true & $1$ \\
\hline
\end{tabular}\end{quote}
</pre>
==Table 2==
<pre>
\begin{quote}\begin{tabular}{|c|c|c|c|c|c|c|}
\multicolumn{7}{c}{Table 2. 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 & $(~)$ & false & $0$ \\
\hline
$f_{1}$ & $f_{0001}$ & & 0 0 0 1 & $(x)(y)$ & neither $x$ nor $y$ & $\lnot x \land \lnot y $ \\
$f_{2}$ & $f_{0010}$ & & 0 0 1 0 & $(x)\ y$ & $y$ and not $x$ & $\lnot x \land y$ \\
$f_{4}$ & $f_{0100}$ & & 0 1 0 0 & $x\ (y)$ & $x$ and not $y$ & $x \land \lnot y$ \\
$f_{8}$ & $f_{1000}$ & & 1 0 0 0 & $x\ y$ & $x$ and $y$ & $x \land y$ \\
\hline
$f_{3}$ & $f_{0011}$ & & 0 0 1 1 & $(x)$ & not $x$ & $\lnot x$ \\
$f_{12}$ & $f_{1100}$ & & 1 1 0 0 & $x$ & $x$ & $x$ \\
\hline
$f_{6}$ & $f_{0110}$ & & 0 1 1 0 & $(x,\ y)$ & $x$ not equal to $y$ & $x \ne y$ \\
$f_{9}$ & $f_{1001}$ & & 1 0 0 1 & $((x,\ y))$ & $x$ equal to $y$ & $x = y$ \\
\hline
$f_{5}$ & $f_{0101}$ & & 0 1 0 1 & $(y)$ & not $y$ & $\lnot y$ \\
$f_{10}$ & $f_{1010}$ & & 1 0 1 0 & $y$ & $y$ & $y$ \\
\hline
$f_{7}$ & $f_{0111}$ & & 0 1 1 1 & $(x\ y)$ & not both $x$ and $y$ & $\lnot x \lor \lnot y$ \\
$f_{11}$ & $f_{1011}$ & & 1 0 1 1 & $(x\ (y))$ & not $x$ without $y$ & $x \Rightarrow y$ \\
$f_{13}$ & $f_{1101}$ & & 1 1 0 1 & $((x)\ y)$ & not $y$ without $x$ & $x \Leftarrow y$ \\
$f_{14}$ & $f_{1110}$ & & 1 1 1 0 & $((x)(y))$ & $x$ or $y$ & $x \lor y$ \\
\hline
$f_{15}$ & $f_{1111}$ & & 1 1 1 1 & $((~))$ & true & $1$ \\
\hline
\end{tabular}\end{quote}
</pre>
=Work Area 1=
=Work Area 1=
