User:Jon Awbrey/MNO

Truth Tables

New Version

 $$\mathcal{L}_1$$ $$\mathcal{L}_2$$ $$\mathcal{L}_3$$ $$\mathcal{L}_4$$ $$p\colon\!$$ $$1~1~1~1~0~0~0~0$$ $$q\colon\!$$ $$1~1~0~0~1~1~0~0$$ $$r\colon\!$$ $$1~0~1~0~1~0~1~0$$ $$\begin{matrix} f_{104} \\[4pt] f_{148} \\[4pt] f_{146} \\[4pt] f_{97} \\[4pt] f_{134} \\[4pt] f_{73} \\[4pt] f_{41} \\[4pt] f_{22} \end{matrix}$$ $$\begin{matrix} f_{01101000} \\[4pt] f_{10010100} \\[4pt] f_{10010010} \\[4pt] f_{01100001} \\[4pt] f_{10000110} \\[4pt] f_{01001001} \\[4pt] f_{00101001} \\[4pt] f_{00010110} \end{matrix}$$ $$\begin{matrix} 0~1~1~0~1~0~0~0 \\[4pt] 1~0~0~1~0~1~0~0 \\[4pt] 1~0~0~1~0~0~1~0 \\[4pt] 0~1~1~0~0~0~0~1 \\[4pt] 1~0~0~0~0~1~1~0 \\[4pt] 0~1~0~0~1~0~0~1 \\[4pt] 0~0~1~0~1~0~0~1 \\[4pt] 0~0~0~1~0~1~1~0 \end{matrix}$$ $$\begin{matrix} \texttt{(~p~,~q~,~r~)} \\[4pt] \texttt{(~p~,~q~,(r))} \\[4pt] \texttt{(~p~,(q),~r~)} \\[4pt] \texttt{(~p~,(q),(r))} \\[4pt] \texttt{((p),~q~,~r~)} \\[4pt] \texttt{((p),~q~,(r))} \\[4pt] \texttt{((p),(q),~r~)} \\[4pt] \texttt{((p),(q),(r))} \end{matrix}$$ $$\begin{matrix} f_{233} \\[4pt] f_{214} \\[4pt] f_{182} \\[4pt] f_{121} \\[4pt] f_{158} \\[4pt] f_{109} \\[4pt] f_{107} \\[4pt] f_{151} \end{matrix}$$ $$\begin{matrix} f_{11101001} \\[4pt] f_{11010110} \\[4pt] f_{10110110} \\[4pt] f_{01111001} \\[4pt] f_{10011110} \\[4pt] f_{01101101} \\[4pt] f_{01101011} \\[4pt] f_{10010111} \end{matrix}$$ $$\begin{matrix} 1~1~1~0~1~0~0~1 \\[4pt] 1~1~0~1~0~1~1~0 \\[4pt] 1~0~1~1~0~1~1~0 \\[4pt] 0~1~1~1~1~0~0~1 \\[4pt] 1~0~0~1~1~1~1~0 \\[4pt] 0~1~1~0~1~1~0~1 \\[4pt] 0~1~1~0~1~0~1~1 \\[4pt] 1~0~0~1~0~1~1~1 \end{matrix}$$ $$\begin{matrix} \texttt{(((p),(q),(r)))} \\[4pt] \texttt{(((p),(q),~r~))} \\[4pt] \texttt{(((p),~q~,(r)))} \\[4pt] \texttt{(((p),~q~,~r~))} \\[4pt] \texttt{((~p~,(q),(r)))} \\[4pt] \texttt{((~p~,(q),~r~))} \\[4pt] \texttt{((~p~,~q~,(r)))} \\[4pt] \texttt{((~p~,~q~,~r~))} \end{matrix}$$

Old Version

 $$\mathcal{L}_1$$ $$\mathcal{L}_2$$ $$\mathcal{L}_3$$ $$\mathcal{L}_4$$ $$p =\!$$ 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

 $$\text{Figure 2.} ~~ \texttt{(} p \texttt{,} q \texttt{,} r \texttt{)}$$
 $$\text{Figure 3.} ~~ \texttt{((} p \texttt{),(} q \texttt{),(} r \texttt{))}$$