Difference between revisions of "User:Jon Awbrey/MNO"
Jon Awbrey (talk | contribs) (→Truth Tables: cleanup) |
Jon Awbrey (talk | contribs) (tweak a bit to raise back to consciousness ...) |
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|+ <math>\text{Table 1.}~~\text{Logical Boundaries and Their Complements}</math> | |+ <math>\text{Table 1.}~~\text{Logical Boundaries and Their Complements}</math> | ||
|- style="background:#f0f0ff" | |- style="background:#f0f0ff" | ||
| − | + | | <math>\mathcal{L}_1</math> | |
| − | + | | <math>\mathcal{L}_2</math> | |
| − | + | | <math>\mathcal{L}_3</math> | |
| − | + | | <math>\mathcal{L}_4</math> | |
|- style="background:#f0f0ff" | |- style="background:#f0f0ff" | ||
| | | | ||
| Line 86: | Line 86: | ||
| | | | ||
<math>\begin{matrix} | <math>\begin{matrix} | ||
| − | ( p , q , r ) | + | \texttt{(~p~,~q~,~r~)} |
\\[4pt] | \\[4pt] | ||
| − | ( p , q , (r)) | + | \texttt{(~p~,~q~,(r))} |
\\[4pt] | \\[4pt] | ||
| − | ( p , (q), r ) | + | \texttt{(~p~,(q),~r~)} |
\\[4pt] | \\[4pt] | ||
| − | ( p , (q), (r)) | + | \texttt{(~p~,(q),(r))} |
\\[4pt] | \\[4pt] | ||
| − | ((p), q , r ) | + | \texttt{((p),~q~,~r~)} |
\\[4pt] | \\[4pt] | ||
| − | ((p), q , (r)) | + | \texttt{((p),~q~,(r))} |
\\[4pt] | \\[4pt] | ||
| − | ((p), (q), r ) | + | \texttt{((p),(q),~r~)} |
\\[4pt] | \\[4pt] | ||
| − | ((p), (q), (r)) | + | \texttt{((p),(q),(r))} |
\end{matrix}</math> | \end{matrix}</math> | ||
|- | |- | ||
| Line 159: | Line 159: | ||
| | | | ||
<math>\begin{matrix} | <math>\begin{matrix} | ||
| − | (((p), (q), (r))) | + | \texttt{(((p),(q),(r)))} |
\\[4pt] | \\[4pt] | ||
| − | (((p), (q), r )) | + | \texttt{(((p),(q),~r~))} |
\\[4pt] | \\[4pt] | ||
| − | (((p), q , (r))) | + | \texttt{(((p),~q~,(r)))} |
\\[4pt] | \\[4pt] | ||
| − | (((p), q , r )) | + | \texttt{(((p),~q~,~r~))} |
\\[4pt] | \\[4pt] | ||
| − | (( p , (q), (r))) | + | \texttt{((~p~,(q),(r)))} |
\\[4pt] | \\[4pt] | ||
| − | (( p , (q), r )) | + | \texttt{((~p~,(q),~r~))} |
\\[4pt] | \\[4pt] | ||
| − | (( p , q , (r))) | + | \texttt{((~p~,~q~,(r)))} |
\\[4pt] | \\[4pt] | ||
| − | (( p , q , r )) | + | \texttt{((~p~,~q~,~r~))} |
\end{matrix}</math> | \end{matrix}</math> | ||
|} | |} | ||
| Line 293: | Line 293: | ||
==Venn Diagrams== | ==Venn Diagrams== | ||
| + | |||
| + | ===New Version=== | ||
| + | |||
| + | {| align="center" cellpadding="10" style="text-align:center" | ||
| + | | | ||
| + | <p>[[Image:Venn Diagram (P,Q,R).jpg|500px]]</p> | ||
| + | <p><math>\text{Figure 2.}~~\texttt{(p, q, r)}</math> | ||
| + | |} | ||
| + | |||
| + | {| align="center" cellpadding="10" style="text-align:center" | ||
| + | | | ||
| + | <p>[[Image:Venn Diagram ((P),(Q),(R)).jpg|500px]]</p> | ||
| + | <p><math>\text{Figure 3.}~~\texttt{((p),(q),(r))}</math> | ||
| + | |} | ||
| + | |||
| + | ===Old Version=== | ||
| + | |||
| + | {| align="center" cellpadding="10" style="text-align:center" | ||
| + | | | ||
| + | <p>[[Image:Minimal Negation Operator 1.jpg|500px]]</p> | ||
| + | <p><math>\text{Figure 2.} ~~ \texttt{(} p \texttt{,} q \texttt{,} r \texttt{)}</math> | ||
| + | |} | ||
| + | |||
| + | {| align="center" cellpadding="10" style="text-align:center" | ||
| + | | | ||
| + | <p>[[Image:Minimal Negation Operator 2.jpg|500px]]</p> | ||
| + | <p><math>\text{Figure 3.} ~~ \texttt{((} p \texttt{),(} q \texttt{),(} r \texttt{))}</math> | ||
| + | |} | ||
| + | |||
| + | * | ||
Latest revision as of 16:10, 28 August 2017
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
|
\(\text{Figure 2.}~~\texttt{(p, q, r)}\) |
.jpg)
|
\(\text{Figure 3.}~~\texttt{((p),(q),(r))}\) |
,(Q),(R)).jpg)
Old Version
|
\(\text{Figure 2.} ~~ \texttt{(} p \texttt{,} q \texttt{,} r \texttt{)}\) |
|
\(\text{Figure 3.} ~~ \texttt{((} p \texttt{),(} q \texttt{),(} r \texttt{))}\) |
