User:Jon Awbrey/MNO
Logical Graphs
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
\(\text{Figure 2.} ~~ \texttt{(} p \texttt{,} q \texttt{,} r \texttt{)}\) |
\(\text{Figure 3.} ~~ \texttt{((} p \texttt{),(} q \texttt{),(} r \texttt{))}\) |