User:Jon Awbrey/MNO

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

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

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

Old Version

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

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