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

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

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