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'differential propositional calculus : appendices'
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| Title of object: |
differential propositional calculus : appendices |
| Canonical Name: |
DifferentialPropositionalCalculusAppendices |
| Type: |
Application |
| Created on: |
2008-06-06 22:05:48 |
| Modified on: |
2008-06-06 23:01:18 |
| Classification: |
msc:03B05, msc:03B42, msc:03B44, msc:34G99, msc:39A12, msc:53A40 |
Preamble:
% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands here
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Content:
\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}
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