MyWikiBiz

Changes

User:Jon Awbrey/MNO (view source)

Revision as of 16:10, 28 August 2017

2,902 bytes added ,  16:10, 28 August 2017
tweak a bit to raise back to consciousness ...
Line 2: Line 2:     
==Truth Tables==
 
==Truth Tables==
 +
 +
===New Version===
    
<br>
 
<br>
    
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%"
 
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%"
−
|+ <math>\text{Table A1.}~~\text{Propositional Forms on Two Variables}</math>
+
|+ <math>\text{Table 1.}~~\text{Logical Boundaries and Their Complements}</math>
 
|- style="background:#f0f0ff"
 
|- style="background:#f0f0ff"
−
| width="15%" |
+
| <math>\mathcal{L}_1</math>
−
<p><math>\mathcal{L}_1</math></p>
+
| <math>\mathcal{L}_2</math>
−
<p><math>\text{Decimal}</math></p>
+
| <math>\mathcal{L}_3</math>
−
| width="15%" |
+
| <math>\mathcal{L}_4</math>
−
<p><math>\mathcal{L}_2</math></p>
  −
<p><math>\text{Binary}</math></p>
  −
| width="15%" |
  −
<p><math>\mathcal{L}_3</math></p>
  −
<p><math>\text{Vector}</math></p>
  −
| width="15%" |
  −
<p><math>\mathcal{L}_4</math></p>
  −
<p><math>\text{Cactus}</math></p>
  −
| width="25%" |
  −
<p><math>\mathcal{L}_5</math></p>
  −
<p><math>\text{English}</math></p>
  −
| width="15%" |
  −
<p><math>\mathcal{L}_6</math></p>
  −
<p><math>\text{Ordinary}</math></p>
   
|- style="background:#f0f0ff"
 
|- style="background:#f0f0ff"
 
| &nbsp;
 
| &nbsp;
 
| align="right" | <math>p\colon\!</math>
 
| align="right" | <math>p\colon\!</math>
−
| <math>1~1~0~0\!</math>
+
| <math>1~1~1~1~0~0~0~0</math>
−
| &nbsp;
  −
| &nbsp;
   
| &nbsp;
 
| &nbsp;
 
|- style="background:#f0f0ff"
 
|- style="background:#f0f0ff"
 
| &nbsp;
 
| &nbsp;
 
| align="right" | <math>q\colon\!</math>
 
| align="right" | <math>q\colon\!</math>
−
| <math>1~0~1~0\!</math>
+
| <math>1~1~0~0~1~1~0~0</math>
 
| &nbsp;
 
| &nbsp;
 +
|- style="background:#f0f0ff"
 
| &nbsp;
 
| &nbsp;
 +
| align="right" | <math>r\colon\!</math>
 +
| <math>1~0~1~0~1~0~1~0</math>
 
| &nbsp;
 
| &nbsp;
 
|-
 
|-
 
|
 
|
 
<math>\begin{matrix}
 
<math>\begin{matrix}
−
f_0
+
f_{104}
 
\\[4pt]
 
\\[4pt]
−
f_1
+
f_{148}
 
\\[4pt]
 
\\[4pt]
−
f_2
+
f_{146}
 
\\[4pt]
 
\\[4pt]
−
f_3
+
f_{97}
 
\\[4pt]
 
\\[4pt]
−
f_4
+
f_{134}
 
\\[4pt]
 
\\[4pt]
−
f_5
+
f_{73}
 
\\[4pt]
 
\\[4pt]
−
f_6
+
f_{41}
 
\\[4pt]
 
\\[4pt]
−
f_7
+
f_{22}
 
\end{matrix}</math>
 
\end{matrix}</math>
 
|
 
|
 
<math>\begin{matrix}
 
<math>\begin{matrix}
−
f_{0000}
+
f_{01101000}
 
\\[4pt]
 
\\[4pt]
−
f_{0001}
+
f_{10010100}
 
\\[4pt]
 
\\[4pt]
−
f_{0010}
+
f_{10010010}
 
\\[4pt]
 
\\[4pt]
−
f_{0011}
+
f_{01100001}
 
\\[4pt]
 
\\[4pt]
−
f_{0100}
+
f_{10000110}
 
\\[4pt]
 
\\[4pt]
−
f_{0101}
+
f_{01001001}
 
\\[4pt]
 
\\[4pt]
−
f_{0110}
+
f_{00101001}
 
\\[4pt]
 
\\[4pt]
−
f_{0111}
+
f_{00010110}
 
\end{matrix}</math>
 
\end{matrix}</math>
 
|
 
|
 
<math>\begin{matrix}
 
<math>\begin{matrix}
−
0~0~0~0
+
0~1~1~0~1~0~0~0
 
\\[4pt]
 
\\[4pt]
−
0~0~0~1
+
1~0~0~1~0~1~0~0
 
\\[4pt]
 
\\[4pt]
−
0~0~1~0
+
1~0~0~1~0~0~1~0
 
\\[4pt]
 
\\[4pt]
−
0~0~1~1
+
0~1~1~0~0~0~0~1
 
\\[4pt]
 
\\[4pt]
−
0~1~0~0
+
1~0~0~0~0~1~1~0
 
\\[4pt]
 
\\[4pt]
−
0~1~0~1
+
0~1~0~0~1~0~0~1
 
\\[4pt]
 
\\[4pt]
−
0~1~1~0
+
0~0~1~0~1~0~0~1
 
\\[4pt]
 
\\[4pt]
−
0~1~1~1
+
0~0~0~1~0~1~1~0
 
\end{matrix}</math>
 
\end{matrix}</math>
 
|
 
|
 
<math>\begin{matrix}
 
<math>\begin{matrix}
−
(~)
+
\texttt{(~p~,~q~,~r~)}
 
\\[4pt]
 
\\[4pt]
−
(p)(q)
+
\texttt{(~p~,~q~,(r))}
 
\\[4pt]
 
\\[4pt]
−
(p)~q~
+
\texttt{(~p~,(q),~r~)}
 
\\[4pt]
 
\\[4pt]
−
(p)~~~
+
\texttt{(~p~,(q),(r))}
 
\\[4pt]
 
\\[4pt]
−
~p~(q)
+
\texttt{((p),~q~,~r~)}
 
\\[4pt]
 
\\[4pt]
−
~~~(q)
+
\texttt{((p),~q~,(r))}
 
\\[4pt]
 
\\[4pt]
−
(p,~q)
+
\texttt{((p),(q),~r~)}
 
\\[4pt]
 
\\[4pt]
−
(p~~q)
+
\texttt{((p),(q),(r))}
 
\end{matrix}</math>
 
\end{matrix}</math>
 +
|-
 
|
 
|
 
<math>\begin{matrix}
 
<math>\begin{matrix}
−
\text{false}
+
f_{233}
 
\\[4pt]
 
\\[4pt]
−
\text{neither}~ p ~\text{nor}~ q
+
f_{214}
 
\\[4pt]
 
\\[4pt]
−
q ~\text{without}~ p
+
f_{182}
 
\\[4pt]
 
\\[4pt]
−
\text{not}~ p
+
f_{121}
 
\\[4pt]
 
\\[4pt]
−
p ~\text{without}~ q
+
f_{158}
 
\\[4pt]
 
\\[4pt]
−
\text{not}~ q
+
f_{109}
 
\\[4pt]
 
\\[4pt]
−
p ~\text{not equal to}~ q
+
f_{107}
 
\\[4pt]
 
\\[4pt]
−
\text{not both}~ p ~\text{and}~ q
+
f_{151}
 
\end{matrix}</math>
 
\end{matrix}</math>
 
|
 
|
 
<math>\begin{matrix}
 
<math>\begin{matrix}
−
0
+
f_{11101001}
 
\\[4pt]
 
\\[4pt]
−
\lnot p \land \lnot q
+
f_{11010110}
 
\\[4pt]
 
\\[4pt]
−
\lnot p \land q
+
f_{10110110}
 
\\[4pt]
 
\\[4pt]
−
\lnot p
+
f_{01111001}
 
\\[4pt]
 
\\[4pt]
−
p \land \lnot q
+
f_{10011110}
 
\\[4pt]
 
\\[4pt]
−
\lnot q
+
f_{01101101}
 
\\[4pt]
 
\\[4pt]
−
p \ne q
+
f_{01101011}
 
\\[4pt]
 
\\[4pt]
−
\lnot p \lor \lnot q
+
f_{10010111}
 
\end{matrix}</math>
 
\end{matrix}</math>
−
|-
   
|
 
|
 
<math>\begin{matrix}
 
<math>\begin{matrix}
−
f_8
+
1~1~1~0~1~0~0~1
 
\\[4pt]
 
\\[4pt]
−
f_9
+
1~1~0~1~0~1~1~0
 
\\[4pt]
 
\\[4pt]
−
f_{10}
+
1~0~1~1~0~1~1~0
 
\\[4pt]
 
\\[4pt]
−
f_{11}
+
0~1~1~1~1~0~0~1
 
\\[4pt]
 
\\[4pt]
−
f_{12}
+
1~0~0~1~1~1~1~0
 
\\[4pt]
 
\\[4pt]
−
f_{13}
+
0~1~1~0~1~1~0~1
 
\\[4pt]
 
\\[4pt]
−
f_{14}
+
0~1~1~0~1~0~1~1
 
\\[4pt]
 
\\[4pt]
−
f_{15}
+
1~0~0~1~0~1~1~1
 
\end{matrix}</math>
 
\end{matrix}</math>
 
|
 
|
 
<math>\begin{matrix}
 
<math>\begin{matrix}
−
f_{1000}
+
\texttt{(((p),(q),(r)))}
 
\\[4pt]
 
\\[4pt]
−
f_{1001}
+
\texttt{(((p),(q),~r~))}
 
\\[4pt]
 
\\[4pt]
−
f_{1010}
+
\texttt{(((p),~q~,(r)))}
 
\\[4pt]
 
\\[4pt]
−
f_{1011}
+
\texttt{(((p),~q~,~r~))}
 
\\[4pt]
 
\\[4pt]
−
f_{1100}
+
\texttt{((~p~,(q),(r)))}
 
\\[4pt]
 
\\[4pt]
−
f_{1101}
+
\texttt{((~p~,(q),~r~))}
 
\\[4pt]
 
\\[4pt]
−
f_{1110}
+
\texttt{((~p~,~q~,(r)))}
 
\\[4pt]
 
\\[4pt]
−
f_{1111}
+
\texttt{((~p~,~q~,~r~))}
 
\end{matrix}</math>
 
\end{matrix}</math>
 +
|}
 +
 +
<br>
 +
 +
===Old Version===
 +
 +
<br>
 +
 +
{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:#f0f0ff; font-weight:bold; text-align:center; width:90%"
 +
|+ <math>\text{Table 1.}~~\text{Logical Boundaries and Their Complements}</math>
 +
| width="25%" | <math>\mathcal{L}_1</math>
 +
| width="25%" | <math>\mathcal{L}_2</math>
 +
| width="25%" | <math>\mathcal{L}_3</math>
 +
| width="25%" | <math>\mathcal{L}_4</math>
 +
|-
 +
| &nbsp;
 +
| align="right" | <math>p =\!</math>
 +
| 1 1 1 1 0 0 0 0
 +
| &nbsp;
 +
|-
 +
| &nbsp;
 +
| align="right" | <math>q =\!</math>
 +
| 1 1 0 0 1 1 0 0
 +
| &nbsp;
 +
|-
 +
| &nbsp;
 +
| align="right" | <math>r =\!</math>
 +
| 1 0 1 0 1 0 1 0
 +
| &nbsp;
 +
|}
 +
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:90%"
 +
|-
 +
| width="25%" | <math>f_{104}\!</math>
 +
| width="25%" | <math>f_{01101000}\!</math>
 +
| width="25%" | 0 1 1 0 1 0 0 0
 +
| width="25%" | <math>( p , q , r )\!</math>
 +
|-
 +
| <math>f_{148}\!</math>
 +
| <math>f_{10010100}\!</math>
 +
| 1 0 0 1 0 1 0 0
 +
| <math>( p , q , (r))\!</math>
 +
|-
 +
| <math>f_{146}\!</math>
 +
| <math>f_{10010010}\!</math>
 +
| 1 0 0 1 0 0 1 0
 +
| <math>( p , (q), r )\!</math>
 +
|-
 +
| <math>f_{97}\!</math>
 +
| <math>f_{01100001}\!</math>
 +
| 0 1 1 0 0 0 0 1
 +
| <math>( p , (q), (r))\!</math>
 +
|-
 +
| <math>f_{134}\!</math>
 +
| <math>f_{10000110}\!</math>
 +
| 1 0 0 0 0 1 1 0
 +
| <math>((p), q , r )\!</math>
 +
|-
 +
| <math>f_{73}\!</math>
 +
| <math>f_{01001001}\!</math>
 +
| 0 1 0 0 1 0 0 1
 +
| <math>((p), q , (r))\!</math>
 +
|-
 +
| <math>f_{41}\!</math>
 +
| <math>f_{00101001}\!</math>
 +
| 0 0 1 0 1 0 0 1
 +
| <math>((p), (q), r )\!</math>
 +
|-
 +
| <math>f_{22}\!</math>
 +
| <math>f_{00010110}\!</math>
 +
| 0 0 0 1 0 1 1 0
 +
| <math>((p), (q), (r))\!</math>
 +
|}
 +
{|  align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:90%"
 +
|-
 +
| width="25%" | <math>f_{233}\!</math>
 +
| width="25%" | <math>f_{11101001}\!</math>
 +
| width="25%" | 1 1 1 0 1 0 0 1
 +
| width="25%" | <math>(((p), (q), (r)))\!</math>
 +
|-
 +
| <math>f_{214}\!</math>
 +
| <math>f_{11010110}\!</math>
 +
| 1 1 0 1 0 1 1 0
 +
| <math>(((p), (q), r ))\!</math>
 +
|-
 +
| <math>f_{182}\!</math>
 +
| <math>f_{10110110}\!</math>
 +
| 1 0 1 1 0 1 1 0
 +
| <math>(((p), q , (r)))\!</math>
 +
|-
 +
| <math>f_{121}\!</math>
 +
| <math>f_{01111001}\!</math>
 +
| 0 1 1 1 1 0 0 1
 +
| <math>(((p), q , r ))\!</math>
 +
|-
 +
| <math>f_{158}\!</math>
 +
| <math>f_{10011110}\!</math>
 +
| 1 0 0 1 1 1 1 0
 +
| <math>(( p , (q), (r)))\!</math>
 +
|-
 +
| <math>f_{109}\!</math>
 +
| <math>f_{01101101}\!</math>
 +
| 0 1 1 0 1 1 0 1
 +
| <math>(( p , (q), r ))\!</math>
 +
|-
 +
| <math>f_{107}\!</math>
 +
| <math>f_{01101011}\!</math>
 +
| 0 1 1 0 1 0 1 1
 +
| <math>(( p , q , (r)))\!</math>
 +
|-
 +
| <math>f_{151}\!</math>
 +
| <math>f_{10010111}\!</math>
 +
| 1 0 0 1 0 1 1 1
 +
| <math>(( p , q , r ))\!</math>
 +
|}
 +
 +
<br>
 +
 +
==Venn Diagrams==
 +
 +
===New Version===
 +
 +
{| align="center" cellpadding="10" style="text-align:center"
 
|
 
|
−
<math>\begin{matrix}
+
<p>[[Image:Venn Diagram (P,Q,R).jpg|500px]]</p>
−
1~0~0~0
+
<p><math>\text{Figure 2.}~~\texttt{(p, q, r)}</math>
−
\\[4pt]
+
|}
−
1~0~0~1
+
 
−
\\[4pt]
+
{| align="center" cellpadding="10" style="text-align:center"
−
1~0~1~0
  −
\\[4pt]
  −
1~0~1~1
  −
\\[4pt]
  −
1~1~0~0
  −
\\[4pt]
  −
1~1~0~1
  −
\\[4pt]
  −
1~1~1~0
  −
\\[4pt]
  −
1~1~1~1
  −
\end{matrix}</math>
   
|
 
|
−
<math>\begin{matrix}
+
<p>[[Image:Venn Diagram ((P),(Q),(R)).jpg|500px]]</p>
−
~~p~~q~~
+
<p><math>\text{Figure 3.}~~\texttt{((p),(q),(r))}</math>
−
\\[4pt]
+
|}
−
((p,~q))
+
 
−
\\[4pt]
+
===Old Version===
−
~~~~~q~~
+
 
−
\\[4pt]
+
{| align="center" cellpadding="10" style="text-align:center"
−
~(p~(q))
  −
\\[4pt]
  −
~~p~~~~~
  −
\\[4pt]
  −
((p)~q)~
  −
\\[4pt]
  −
((p)(q))
  −
\\[4pt]
  −
((~))
  −
\end{matrix}</math>
   
|
 
|
−
<math>\begin{matrix}
+
<p>[[Image:Minimal Negation Operator 1.jpg|500px]]</p>
−
p ~\text{and}~ q
+
<p><math>\text{Figure 2.} ~~ \texttt{(} p \texttt{,} q \texttt{,} r \texttt{)}</math>
−
\\[4pt]
+
|}
−
p ~\text{equal to}~ q
+
 
−
\\[4pt]
+
{| align="center" cellpadding="10" style="text-align:center"
−
q
  −
\\[4pt]
  −
\text{not}~ p ~\text{without}~ q
  −
\\[4pt]
  −
p
  −
\\[4pt]
  −
\text{not}~ q ~\text{without}~ p
  −
\\[4pt]
  −
p ~\text{or}~ q
  −
\\[4pt]
  −
\text{true}
  −
\end{matrix}</math>
   
|
 
|
−
<math>\begin{matrix}
+
<p>[[Image:Minimal Negation Operator 2.jpg|500px]]</p>
−
p \land q
+
<p><math>\text{Figure 3.} ~~ \texttt{((} p \texttt{),(} q \texttt{),(} r \texttt{))}</math>
−
\\[4pt]
  −
p = q
  −
\\[4pt]
  −
q
  −
\\[4pt]
  −
p \Rightarrow q
  −
\\[4pt]
  −
p
  −
\\[4pt]
  −
p \Leftarrow q
  −
\\[4pt]
  −
p \lor q
  −
\\[4pt]
  −
1
  −
\end{matrix}</math>
   
|}
 
|}
   −
<br>
+
*
−
 
  −
==Venn Diagrams==
 
Jon Awbrey
12,080

edits

Retrieved from "https://mywikibiz.com/Special:MobileDiff/90900...468023"