User:Jon Awbrey/MNO

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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

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