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

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==Truth Tables==
 
==Truth Tables==
  
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===Version 3?===
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===New Version===
  
 
<br>
 
<br>
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<math>\begin{matrix}
 
<math>\begin{matrix}
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\texttt{( p , q , r )}
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\texttt{(~p~,~q~,~r~)}
 
\\[4pt]
 
\\[4pt]
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\texttt{( p , q , (r))}
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\texttt{(~p~,~q~,(r))}
 
\\[4pt]
 
\\[4pt]
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\texttt{( p , (q), r )}
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\texttt{(~p~,(q),~r~)}
 
\\[4pt]
 
\\[4pt]
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\texttt{( p , (q), (r))}
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\texttt{(~p~,(q),(r))}
 
\\[4pt]
 
\\[4pt]
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\texttt{((p), q , r )}
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\texttt{((p),~q~,~r~)}
 
\\[4pt]
 
\\[4pt]
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\texttt{((p), q , (r))}
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\texttt{((p),~q~,(r))}
 
\\[4pt]
 
\\[4pt]
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\texttt{((p), (q), r )}
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\texttt{((p),(q),~r~)}
 
\\[4pt]
 
\\[4pt]
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\texttt{((p), (q), (r))}
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\texttt{((p),(q),(r))}
 
\end{matrix}</math>
 
\end{matrix}</math>
 
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<math>\begin{matrix}
 
<math>\begin{matrix}
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\texttt{(((p), (q), (r)))}
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\texttt{(((p),(q),(r)))}
 
\\[4pt]
 
\\[4pt]
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\texttt{(((p), (q), r ))}
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\texttt{(((p),(q),~r~))}
 
\\[4pt]
 
\\[4pt]
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\texttt{(((p), q , (r)))}
+
\texttt{(((p),~q~,(r)))}
 
\\[4pt]
 
\\[4pt]
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\texttt{(((p), q , r ))}
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\texttt{(((p),~q~,~r~))}
 
\\[4pt]
 
\\[4pt]
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\texttt{(( p , (q), (r)))}
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\texttt{((~p~,(q),(r)))}
 
\\[4pt]
 
\\[4pt]
−
\texttt{(( p , (q), r ))}
+
\texttt{((~p~,(q),~r~))}
 
\\[4pt]
 
\\[4pt]
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\texttt{(( p , q , (r)))}
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\texttt{((~p~,~q~,(r)))}
 
\\[4pt]
 
\\[4pt]
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\texttt{(( p , q , r ))}
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\texttt{((~p~,~q~,~r~))}
 
\end{matrix}</math>
 
\end{matrix}</math>
 
|}
 
|}
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<br>
 
<br>
  
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===Version 2===
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===Old Version===
−
 
 
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<br>
 
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%"
 
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|+ <math>\text{Table 1.}~~\text{Logical Boundaries and Their Complements}</math>
 
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|- style="background:#f0f0ff"
 
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| <math>\mathcal{L}_1</math>
 
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| <math>\mathcal{L}_2</math>
 
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| <math>\mathcal{L}_3</math>
 
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| <math>\mathcal{L}_4</math>
 
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|- style="background:#f0f0ff"
 
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| &nbsp;
 
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| align="right" | <math>p\colon\!</math>
 
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| <math>1~1~1~1~0~0~0~0</math>
 
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| &nbsp;
 
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|- style="background:#f0f0ff"
 
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| &nbsp;
 
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| align="right" | <math>q\colon\!</math>
 
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| <math>1~1~0~0~1~1~0~0</math>
 
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| &nbsp;
 
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|- style="background:#f0f0ff"
 
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| &nbsp;
 
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| align="right" | <math>r\colon\!</math>
 
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| <math>1~0~1~0~1~0~1~0</math>
 
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| &nbsp;
 
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|-
 
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|
 
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<math>\begin{matrix}
 
−
f_{104}
 
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\\[4pt]
 
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f_{148}
 
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\\[4pt]
 
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f_{146}
 
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\\[4pt]
 
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f_{97}
 
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\\[4pt]
 
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f_{134}
 
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\\[4pt]
 
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f_{73}
 
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\\[4pt]
 
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f_{41}
 
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\\[4pt]
 
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f_{22}
 
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\end{matrix}</math>
 
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|
 
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<math>\begin{matrix}
 
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f_{01101000}
 
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\\[4pt]
 
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f_{10010100}
 
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\\[4pt]
 
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f_{10010010}
 
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\\[4pt]
 
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f_{01100001}
 
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\\[4pt]
 
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f_{10000110}
 
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\\[4pt]
 
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f_{01001001}
 
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\\[4pt]
 
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f_{00101001}
 
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\\[4pt]
 
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f_{00010110}
 
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\end{matrix}</math>
 
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|
 
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<math>\begin{matrix}
 
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0~1~1~0~1~0~0~0
 
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\\[4pt]
 
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1~0~0~1~0~1~0~0
 
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\\[4pt]
 
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1~0~0~1~0~0~1~0
 
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\\[4pt]
 
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0~1~1~0~0~0~0~1
 
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\\[4pt]
 
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1~0~0~0~0~1~1~0
 
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\\[4pt]
 
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0~1~0~0~1~0~0~1
 
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\\[4pt]
 
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0~0~1~0~1~0~0~1
 
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\\[4pt]
 
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0~0~0~1~0~1~1~0
 
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\end{matrix}</math>
 
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|
 
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<math>\begin{matrix}
 
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( p , q , r )
 
−
\\[4pt]
 
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( p , q , (r))
 
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\\[4pt]
 
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( p , (q), r )
 
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\\[4pt]
 
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( p , (q), (r))
 
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\\[4pt]
 
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((p), q , r )
 
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\\[4pt]
 
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((p), q , (r))
 
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\\[4pt]
 
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((p), (q), r )
 
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\\[4pt]
 
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((p), (q), (r))
 
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\end{matrix}</math>
 
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|-
 
−
|
 
−
<math>\begin{matrix}
 
−
f_{233}
 
−
\\[4pt]
 
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f_{214}
 
−
\\[4pt]
 
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f_{182}
 
−
\\[4pt]
 
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f_{121}
 
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\\[4pt]
 
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f_{158}
 
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\\[4pt]
 
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f_{109}
 
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\\[4pt]
 
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f_{107}
 
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\\[4pt]
 
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f_{151}
 
−
\end{matrix}</math>
 
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|
 
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<math>\begin{matrix}
 
−
f_{11101001}
 
−
\\[4pt]
 
−
f_{11010110}
 
−
\\[4pt]
 
−
f_{10110110}
 
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\\[4pt]
 
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f_{01111001}
 
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\\[4pt]
 
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f_{10011110}
 
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\\[4pt]
 
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f_{01101101}
 
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\\[4pt]
 
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f_{01101011}
 
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\\[4pt]
 
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f_{10010111}
 
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\end{matrix}</math>
 
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|
 
−
<math>\begin{matrix}
 
−
1~1~1~0~1~0~0~1
 
−
\\[4pt]
 
−
1~1~0~1~0~1~1~0
 
−
\\[4pt]
 
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1~0~1~1~0~1~1~0
 
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\\[4pt]
 
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0~1~1~1~1~0~0~1
 
−
\\[4pt]
 
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1~0~0~1~1~1~1~0
 
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\\[4pt]
 
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0~1~1~0~1~1~0~1
 
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\\[4pt]
 
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0~1~1~0~1~0~1~1
 
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\\[4pt]
 
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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 ))
 
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\end{matrix}</math>
 
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|}
 
−
 
 
−
<br>
 
−
 
 
−
===Version 1===
 
  
 
<br>
 
<br>
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<p>[[Image:Venn Diagram (P,Q,R).jpg|500px]]</p>
 
<p>[[Image:Venn Diagram (P,Q,R).jpg|500px]]</p>
−
<p><math>\text{Figure 2.} ~~ \texttt{(} p \texttt{,} q \texttt{,} r \texttt{)}</math>
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<p><math>\text{Figure 2.}~~\texttt{(p, q, r)}</math>
 
|}
 
|}
  
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<p>[[Image:Venn Diagram ((P),(Q),(R)).jpg|500px]]</p>
 
<p>[[Image:Venn Diagram ((P),(Q),(R)).jpg|500px]]</p>
−
<p><math>\text{Figure 3.} ~~ \texttt{((} p \texttt{),(} q \texttt{),(} r \texttt{))}</math>
+
<p><math>\text{Figure 3.}~~\texttt{((p),(q),(r))}</math>
 
|}
 
|}
  
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<p><math>\text{Figure 3.} ~~ \texttt{((} p \texttt{),(} q \texttt{),(} r \texttt{))}</math>
 
<p><math>\text{Figure 3.} ~~ \texttt{((} p \texttt{),(} q \texttt{),(} r \texttt{))}</math>
 
|}
 
|}
 +
 +
*

Latest revision as of 16:10, 28 August 2017

Logical Graphs

Truth Tables

New Version


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

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

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

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

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

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

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

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

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


Old Version


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

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

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

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

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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