Difference between revisions of "User:Jon Awbrey/MNO"

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==Truth Tables==
 
==Truth Tables==
  
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===New Version===
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===Version 3?===
  
 
<br>
 
<br>
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<br>
 
<br>
  
−
===Old Version===
+
===Version 2===
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 +
<br>
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 +
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%"
 +
|+ <math>\text{Table 1.}~~\text{Logical Boundaries and Their Complements}</math>
 +
|- style="background:#f0f0ff"
 +
| <math>\mathcal{L}_1</math>
 +
| <math>\mathcal{L}_2</math>
 +
| <math>\mathcal{L}_3</math>
 +
| <math>\mathcal{L}_4</math>
 +
|- style="background:#f0f0ff"
 +
| &nbsp;
 +
| align="right" | <math>p\colon\!</math>
 +
| <math>1~1~1~1~0~0~0~0</math>
 +
| &nbsp;
 +
|- style="background:#f0f0ff"
 +
| &nbsp;
 +
| align="right" | <math>q\colon\!</math>
 +
| <math>1~1~0~0~1~1~0~0</math>
 +
| &nbsp;
 +
|- style="background:#f0f0ff"
 +
| &nbsp;
 +
| align="right" | <math>r\colon\!</math>
 +
| <math>1~0~1~0~1~0~1~0</math>
 +
| &nbsp;
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|-
 +
|
 +
<math>\begin{matrix}
 +
f_{104}
 +
\\[4pt]
 +
f_{148}
 +
\\[4pt]
 +
f_{146}
 +
\\[4pt]
 +
f_{97}
 +
\\[4pt]
 +
f_{134}
 +
\\[4pt]
 +
f_{73}
 +
\\[4pt]
 +
f_{41}
 +
\\[4pt]
 +
f_{22}
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
f_{01101000}
 +
\\[4pt]
 +
f_{10010100}
 +
\\[4pt]
 +
f_{10010010}
 +
\\[4pt]
 +
f_{01100001}
 +
\\[4pt]
 +
f_{10000110}
 +
\\[4pt]
 +
f_{01001001}
 +
\\[4pt]
 +
f_{00101001}
 +
\\[4pt]
 +
f_{00010110}
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
0~1~1~0~1~0~0~0
 +
\\[4pt]
 +
1~0~0~1~0~1~0~0
 +
\\[4pt]
 +
1~0~0~1~0~0~1~0
 +
\\[4pt]
 +
0~1~1~0~0~0~0~1
 +
\\[4pt]
 +
1~0~0~0~0~1~1~0
 +
\\[4pt]
 +
0~1~0~0~1~0~0~1
 +
\\[4pt]
 +
0~0~1~0~1~0~0~1
 +
\\[4pt]
 +
0~0~0~1~0~1~1~0
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
( p , q , r )
 +
\\[4pt]
 +
( p , q , (r))
 +
\\[4pt]
 +
( p , (q), r )
 +
\\[4pt]
 +
( p , (q), (r))
 +
\\[4pt]
 +
((p), q , r )
 +
\\[4pt]
 +
((p), q , (r))
 +
\\[4pt]
 +
((p), (q), r )
 +
\\[4pt]
 +
((p), (q), (r))
 +
\end{matrix}</math>
 +
|-
 +
|
 +
<math>\begin{matrix}
 +
f_{233}
 +
\\[4pt]
 +
f_{214}
 +
\\[4pt]
 +
f_{182}
 +
\\[4pt]
 +
f_{121}
 +
\\[4pt]
 +
f_{158}
 +
\\[4pt]
 +
f_{109}
 +
\\[4pt]
 +
f_{107}
 +
\\[4pt]
 +
f_{151}
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
f_{11101001}
 +
\\[4pt]
 +
f_{11010110}
 +
\\[4pt]
 +
f_{10110110}
 +
\\[4pt]
 +
f_{01111001}
 +
\\[4pt]
 +
f_{10011110}
 +
\\[4pt]
 +
f_{01101101}
 +
\\[4pt]
 +
f_{01101011}
 +
\\[4pt]
 +
f_{10010111}
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
1~1~1~0~1~0~0~1
 +
\\[4pt]
 +
1~1~0~1~0~1~1~0
 +
\\[4pt]
 +
1~0~1~1~0~1~1~0
 +
\\[4pt]
 +
0~1~1~1~1~0~0~1
 +
\\[4pt]
 +
1~0~0~1~1~1~1~0
 +
\\[4pt]
 +
0~1~1~0~1~1~0~1
 +
\\[4pt]
 +
0~1~1~0~1~0~1~1
 +
\\[4pt]
 +
1~0~0~1~0~1~1~1
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
(((p), (q), (r)))
 +
\\[4pt]
 +
(((p), (q), r ))
 +
\\[4pt]
 +
(((p), q , (r)))
 +
\\[4pt]
 +
(((p), q , r ))
 +
\\[4pt]
 +
(( p , (q), (r)))
 +
\\[4pt]
 +
(( p , (q), r ))
 +
\\[4pt]
 +
(( p , q , (r)))
 +
\\[4pt]
 +
(( p , q , r ))
 +
\end{matrix}</math>
 +
|}
 +
 
 +
<br>
 +
 
 +
===Version 1===
  
 
<br>
 
<br>

Revision as of 16:16, 23 August 2009

Logical Graphs

Truth Tables

Version 3?


\(\text{Table 1.}~~\text{Logical Boundaries and Their Complements}\)
\(\mathcal{L}_1\) \(\mathcal{L}_2\) \(\mathcal{L}_3\) \(\mathcal{L}_4\)
  \(p\colon\!\) \(1~1~1~1~0~0~0~0\)  
  \(q\colon\!\) \(1~1~0~0~1~1~0~0\)  
  \(r\colon\!\) \(1~0~1~0~1~0~1~0\)  

\(\begin{matrix} f_{104} \\[4pt] f_{148} \\[4pt] f_{146} \\[4pt] f_{97} \\[4pt] f_{134} \\[4pt] f_{73} \\[4pt] f_{41} \\[4pt] f_{22} \end{matrix}\)

\(\begin{matrix} f_{01101000} \\[4pt] f_{10010100} \\[4pt] f_{10010010} \\[4pt] f_{01100001} \\[4pt] f_{10000110} \\[4pt] f_{01001001} \\[4pt] f_{00101001} \\[4pt] f_{00010110} \end{matrix}\)

\(\begin{matrix} 0~1~1~0~1~0~0~0 \\[4pt] 1~0~0~1~0~1~0~0 \\[4pt] 1~0~0~1~0~0~1~0 \\[4pt] 0~1~1~0~0~0~0~1 \\[4pt] 1~0~0~0~0~1~1~0 \\[4pt] 0~1~0~0~1~0~0~1 \\[4pt] 0~0~1~0~1~0~0~1 \\[4pt] 0~0~0~1~0~1~1~0 \end{matrix}\)

\(\begin{matrix} ( p , q , r ) \\[4pt] ( p , q , (r)) \\[4pt] ( p , (q), r ) \\[4pt] ( p , (q), (r)) \\[4pt] ((p), q , r ) \\[4pt] ((p), q , (r)) \\[4pt] ((p), (q), r ) \\[4pt] ((p), (q), (r)) \end{matrix}\)

\(\begin{matrix} f_{233} \\[4pt] f_{214} \\[4pt] f_{182} \\[4pt] f_{121} \\[4pt] f_{158} \\[4pt] f_{109} \\[4pt] f_{107} \\[4pt] f_{151} \end{matrix}\)

\(\begin{matrix} f_{11101001} \\[4pt] f_{11010110} \\[4pt] f_{10110110} \\[4pt] f_{01111001} \\[4pt] f_{10011110} \\[4pt] f_{01101101} \\[4pt] f_{01101011} \\[4pt] f_{10010111} \end{matrix}\)

\(\begin{matrix} 1~1~1~0~1~0~0~1 \\[4pt] 1~1~0~1~0~1~1~0 \\[4pt] 1~0~1~1~0~1~1~0 \\[4pt] 0~1~1~1~1~0~0~1 \\[4pt] 1~0~0~1~1~1~1~0 \\[4pt] 0~1~1~0~1~1~0~1 \\[4pt] 0~1~1~0~1~0~1~1 \\[4pt] 1~0~0~1~0~1~1~1 \end{matrix}\)

\(\begin{matrix} (((p), (q), (r))) \\[4pt] (((p), (q), r )) \\[4pt] (((p), q , (r))) \\[4pt] (((p), q , r )) \\[4pt] (( p , (q), (r))) \\[4pt] (( p , (q), r )) \\[4pt] (( p , q , (r))) \\[4pt] (( p , q , r )) \end{matrix}\)


Version 2


\(\text{Table 1.}~~\text{Logical Boundaries and Their Complements}\)
\(\mathcal{L}_1\) \(\mathcal{L}_2\) \(\mathcal{L}_3\) \(\mathcal{L}_4\)
  \(p\colon\!\) \(1~1~1~1~0~0~0~0\)  
  \(q\colon\!\) \(1~1~0~0~1~1~0~0\)  
  \(r\colon\!\) \(1~0~1~0~1~0~1~0\)  

\(\begin{matrix} f_{104} \\[4pt] f_{148} \\[4pt] f_{146} \\[4pt] f_{97} \\[4pt] f_{134} \\[4pt] f_{73} \\[4pt] f_{41} \\[4pt] f_{22} \end{matrix}\)

\(\begin{matrix} f_{01101000} \\[4pt] f_{10010100} \\[4pt] f_{10010010} \\[4pt] f_{01100001} \\[4pt] f_{10000110} \\[4pt] f_{01001001} \\[4pt] f_{00101001} \\[4pt] f_{00010110} \end{matrix}\)

\(\begin{matrix} 0~1~1~0~1~0~0~0 \\[4pt] 1~0~0~1~0~1~0~0 \\[4pt] 1~0~0~1~0~0~1~0 \\[4pt] 0~1~1~0~0~0~0~1 \\[4pt] 1~0~0~0~0~1~1~0 \\[4pt] 0~1~0~0~1~0~0~1 \\[4pt] 0~0~1~0~1~0~0~1 \\[4pt] 0~0~0~1~0~1~1~0 \end{matrix}\)

\(\begin{matrix} ( p , q , r ) \\[4pt] ( p , q , (r)) \\[4pt] ( p , (q), r ) \\[4pt] ( p , (q), (r)) \\[4pt] ((p), q , r ) \\[4pt] ((p), q , (r)) \\[4pt] ((p), (q), r ) \\[4pt] ((p), (q), (r)) \end{matrix}\)

\(\begin{matrix} f_{233} \\[4pt] f_{214} \\[4pt] f_{182} \\[4pt] f_{121} \\[4pt] f_{158} \\[4pt] f_{109} \\[4pt] f_{107} \\[4pt] f_{151} \end{matrix}\)

\(\begin{matrix} f_{11101001} \\[4pt] f_{11010110} \\[4pt] f_{10110110} \\[4pt] f_{01111001} \\[4pt] f_{10011110} \\[4pt] f_{01101101} \\[4pt] f_{01101011} \\[4pt] f_{10010111} \end{matrix}\)

\(\begin{matrix} 1~1~1~0~1~0~0~1 \\[4pt] 1~1~0~1~0~1~1~0 \\[4pt] 1~0~1~1~0~1~1~0 \\[4pt] 0~1~1~1~1~0~0~1 \\[4pt] 1~0~0~1~1~1~1~0 \\[4pt] 0~1~1~0~1~1~0~1 \\[4pt] 0~1~1~0~1~0~1~1 \\[4pt] 1~0~0~1~0~1~1~1 \end{matrix}\)

\(\begin{matrix} (((p), (q), (r))) \\[4pt] (((p), (q), r )) \\[4pt] (((p), q , (r))) \\[4pt] (((p), q , r )) \\[4pt] (( p , (q), (r))) \\[4pt] (( p , (q), r )) \\[4pt] (( p , q , (r))) \\[4pt] (( p , q , r )) \end{matrix}\)


Version 1


\(\text{Table 1.}~~\text{Logical Boundaries and Their Complements}\)
\(\mathcal{L}_1\) \(\mathcal{L}_2\) \(\mathcal{L}_3\) \(\mathcal{L}_4\)
  \(p =\!\) 1 1 1 1 0 0 0 0  
  \(q =\!\) 1 1 0 0 1 1 0 0  
  \(r =\!\) 1 0 1 0 1 0 1 0  
\(f_{104}\!\) \(f_{01101000}\!\) 0 1 1 0 1 0 0 0 \(( p , q , r )\!\)
\(f_{148}\!\) \(f_{10010100}\!\) 1 0 0 1 0 1 0 0 \(( p , q , (r))\!\)
\(f_{146}\!\) \(f_{10010010}\!\) 1 0 0 1 0 0 1 0 \(( p , (q), r )\!\)
\(f_{97}\!\) \(f_{01100001}\!\) 0 1 1 0 0 0 0 1 \(( p , (q), (r))\!\)
\(f_{134}\!\) \(f_{10000110}\!\) 1 0 0 0 0 1 1 0 \(((p), q , r )\!\)
\(f_{73}\!\) \(f_{01001001}\!\) 0 1 0 0 1 0 0 1 \(((p), q , (r))\!\)
\(f_{41}\!\) \(f_{00101001}\!\) 0 0 1 0 1 0 0 1 \(((p), (q), r )\!\)
\(f_{22}\!\) \(f_{00010110}\!\) 0 0 0 1 0 1 1 0 \(((p), (q), (r))\!\)
\(f_{233}\!\) \(f_{11101001}\!\) 1 1 1 0 1 0 0 1 \((((p), (q), (r)))\!\)
\(f_{214}\!\) \(f_{11010110}\!\) 1 1 0 1 0 1 1 0 \((((p), (q), r ))\!\)
\(f_{182}\!\) \(f_{10110110}\!\) 1 0 1 1 0 1 1 0 \((((p), q , (r)))\!\)
\(f_{121}\!\) \(f_{01111001}\!\) 0 1 1 1 1 0 0 1 \((((p), q , r ))\!\)
\(f_{158}\!\) \(f_{10011110}\!\) 1 0 0 1 1 1 1 0 \((( p , (q), (r)))\!\)
\(f_{109}\!\) \(f_{01101101}\!\) 0 1 1 0 1 1 0 1 \((( p , (q), r ))\!\)
\(f_{107}\!\) \(f_{01101011}\!\) 0 1 1 0 1 0 1 1 \((( p , q , (r)))\!\)
\(f_{151}\!\) \(f_{10010111}\!\) 1 0 0 1 0 1 1 1 \((( p , q , r ))\!\)


Venn Diagrams

New Version

Venn Diagram (P,Q,R).jpg

\(\text{Figure 2.} ~~ \texttt{(} p \texttt{,} q \texttt{,} r \texttt{)}\)

Venn Diagram ((P),(Q),(R)).jpg

\(\text{Figure 3.} ~~ \texttt{((} p \texttt{),(} q \texttt{),(} r \texttt{))}\)

Old Version

Minimal Negation Operator 1.jpg

\(\text{Figure 2.} ~~ \texttt{(} p \texttt{,} q \texttt{,} r \texttt{)}\)

Minimal Negation Operator 2.jpg

\(\text{Figure 3.} ~~ \texttt{((} p \texttt{),(} q \texttt{),(} r \texttt{))}\)

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