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User:Jon Awbrey/MNO (view source)

Revision as of 16:10, 28 August 2017

6,042 bytes added ,  16:10, 28 August 2017
tweak a bit to raise back to consciousness ...
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==Truth Tables==
 
==Truth Tables==
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===New Version===
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<br>
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%"
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|+ <math>\text{Table 1.}~~\text{Logical Boundaries and Their Complements}</math>
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|- style="background:#f0f0ff"
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| <math>\mathcal{L}_1</math>
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| <math>\mathcal{L}_2</math>
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| <math>\mathcal{L}_3</math>
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| <math>\mathcal{L}_4</math>
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|- style="background:#f0f0ff"
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| &nbsp;
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| align="right" | <math>p\colon\!</math>
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| <math>1~1~1~1~0~0~0~0</math>
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| &nbsp;
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|- style="background:#f0f0ff"
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| &nbsp;
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| align="right" | <math>q\colon\!</math>
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| <math>1~1~0~0~1~1~0~0</math>
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| &nbsp;
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|- style="background:#f0f0ff"
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| &nbsp;
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| align="right" | <math>r\colon\!</math>
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| <math>1~0~1~0~1~0~1~0</math>
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| &nbsp;
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|-
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|
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<math>\begin{matrix}
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f_{104}
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\\[4pt]
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f_{148}
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\\[4pt]
 +
f_{146}
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\\[4pt]
 +
f_{97}
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\\[4pt]
 +
f_{134}
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\\[4pt]
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f_{73}
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\\[4pt]
 +
f_{41}
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\\[4pt]
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f_{22}
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\end{matrix}</math>
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|
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<math>\begin{matrix}
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f_{01101000}
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\\[4pt]
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f_{10010100}
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\\[4pt]
 +
f_{10010010}
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\\[4pt]
 +
f_{01100001}
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\\[4pt]
 +
f_{10000110}
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\\[4pt]
 +
f_{01001001}
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\\[4pt]
 +
f_{00101001}
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\\[4pt]
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f_{00010110}
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\end{matrix}</math>
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|
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<math>\begin{matrix}
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0~1~1~0~1~0~0~0
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\\[4pt]
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1~0~0~1~0~1~0~0
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\\[4pt]
 +
1~0~0~1~0~0~1~0
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\\[4pt]
 +
0~1~1~0~0~0~0~1
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\\[4pt]
 +
1~0~0~0~0~1~1~0
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\\[4pt]
 +
0~1~0~0~1~0~0~1
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\\[4pt]
 +
0~0~1~0~1~0~0~1
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\\[4pt]
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0~0~0~1~0~1~1~0
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\end{matrix}</math>
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|
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<math>\begin{matrix}
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\texttt{(~p~,~q~,~r~)}
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\\[4pt]
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\texttt{(~p~,~q~,(r))}
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\\[4pt]
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\texttt{(~p~,(q),~r~)}
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\\[4pt]
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\texttt{(~p~,(q),(r))}
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\\[4pt]
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\texttt{((p),~q~,~r~)}
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\\[4pt]
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\texttt{((p),~q~,(r))}
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\\[4pt]
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\texttt{((p),(q),~r~)}
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\\[4pt]
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\texttt{((p),(q),(r))}
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\end{matrix}</math>
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|-
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|
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<math>\begin{matrix}
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f_{233}
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\\[4pt]
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f_{214}
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\\[4pt]
 +
f_{182}
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\\[4pt]
 +
f_{121}
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\\[4pt]
 +
f_{158}
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\\[4pt]
 +
f_{109}
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\\[4pt]
 +
f_{107}
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\\[4pt]
 +
f_{151}
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\end{matrix}</math>
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|
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<math>\begin{matrix}
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f_{11101001}
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\\[4pt]
 +
f_{11010110}
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\\[4pt]
 +
f_{10110110}
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\\[4pt]
 +
f_{01111001}
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\\[4pt]
 +
f_{10011110}
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\\[4pt]
 +
f_{01101101}
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\\[4pt]
 +
f_{01101011}
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\\[4pt]
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f_{10010111}
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\end{matrix}</math>
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|
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<math>\begin{matrix}
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1~1~1~0~1~0~0~1
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\\[4pt]
 +
1~1~0~1~0~1~1~0
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\\[4pt]
 +
1~0~1~1~0~1~1~0
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\\[4pt]
 +
0~1~1~1~1~0~0~1
 +
\\[4pt]
 +
1~0~0~1~1~1~1~0
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\\[4pt]
 +
0~1~1~0~1~1~0~1
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\\[4pt]
 +
0~1~1~0~1~0~1~1
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\\[4pt]
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1~0~0~1~0~1~1~1
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\end{matrix}</math>
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|
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<math>\begin{matrix}
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\texttt{(((p),(q),(r)))}
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\\[4pt]
 +
\texttt{(((p),(q),~r~))}
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\\[4pt]
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\texttt{(((p),~q~,(r)))}
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\\[4pt]
 +
\texttt{(((p),~q~,~r~))}
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\\[4pt]
 +
\texttt{((~p~,(q),(r)))}
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\\[4pt]
 +
\texttt{((~p~,(q),~r~))}
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\\[4pt]
 +
\texttt{((~p~,~q~,(r)))}
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\\[4pt]
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\texttt{((~p~,~q~,~r~))}
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\end{matrix}</math>
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|}
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<br>
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 +
===Old Version===
 +
 +
<br>
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 +
{| 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>
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| width="25%" | <math>\mathcal{L}_2</math>
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| width="25%" | <math>\mathcal{L}_3</math>
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| width="25%" | <math>\mathcal{L}_4</math>
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|-
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| &nbsp;
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| align="right" | <math>p =\!</math>
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| 1 1 1 1 0 0 0 0
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| &nbsp;
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|-
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| &nbsp;
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| align="right" | <math>q =\!</math>
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| 1 1 0 0 1 1 0 0
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| &nbsp;
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|-
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| &nbsp;
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| align="right" | <math>r =\!</math>
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| 1 0 1 0 1 0 1 0
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| &nbsp;
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|}
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{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:90%"
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|-
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| width="25%" | <math>f_{104}\!</math>
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| width="25%" | <math>f_{01101000}\!</math>
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| width="25%" | 0 1 1 0 1 0 0 0
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| width="25%" | <math>( p , q , r )\!</math>
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|-
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| <math>f_{148}\!</math>
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| <math>f_{10010100}\!</math>
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| 1 0 0 1 0 1 0 0
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| <math>( p , q , (r))\!</math>
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|-
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| <math>f_{146}\!</math>
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| <math>f_{10010010}\!</math>
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| 1 0 0 1 0 0 1 0
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| <math>( p , (q), r )\!</math>
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|-
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| <math>f_{97}\!</math>
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| <math>f_{01100001}\!</math>
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| 0 1 1 0 0 0 0 1
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| <math>( p , (q), (r))\!</math>
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|-
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| <math>f_{134}\!</math>
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| <math>f_{10000110}\!</math>
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| 1 0 0 0 0 1 1 0
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| <math>((p), q , r )\!</math>
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|-
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| <math>f_{73}\!</math>
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| <math>f_{01001001}\!</math>
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| 0 1 0 0 1 0 0 1
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| <math>((p), q , (r))\!</math>
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|-
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| <math>f_{41}\!</math>
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| <math>f_{00101001}\!</math>
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| 0 0 1 0 1 0 0 1
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| <math>((p), (q), r )\!</math>
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|-
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| <math>f_{22}\!</math>
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| <math>f_{00010110}\!</math>
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| 0 0 0 1 0 1 1 0
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| <math>((p), (q), (r))\!</math>
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|}
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{|  align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:90%"
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|-
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| width="25%" | <math>f_{233}\!</math>
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| width="25%" | <math>f_{11101001}\!</math>
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| width="25%" | 1 1 1 0 1 0 0 1
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| width="25%" | <math>(((p), (q), (r)))\!</math>
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|-
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| <math>f_{214}\!</math>
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| <math>f_{11010110}\!</math>
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| 1 1 0 1 0 1 1 0
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| <math>(((p), (q), r ))\!</math>
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|-
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| <math>f_{182}\!</math>
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| <math>f_{10110110}\!</math>
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| 1 0 1 1 0 1 1 0
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| <math>(((p), q , (r)))\!</math>
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|-
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| <math>f_{121}\!</math>
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| <math>f_{01111001}\!</math>
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| 0 1 1 1 1 0 0 1
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| <math>(((p), q , r ))\!</math>
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|-
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| <math>f_{158}\!</math>
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| <math>f_{10011110}\!</math>
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| 1 0 0 1 1 1 1 0
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| <math>(( p , (q), (r)))\!</math>
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|-
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| <math>f_{109}\!</math>
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| <math>f_{01101101}\!</math>
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| 0 1 1 0 1 1 0 1
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| <math>(( p , (q), r ))\!</math>
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|-
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| <math>f_{107}\!</math>
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| <math>f_{01101011}\!</math>
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| 0 1 1 0 1 0 1 1
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| <math>(( p , q , (r)))\!</math>
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|-
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| <math>f_{151}\!</math>
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| <math>f_{10010111}\!</math>
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| 1 0 0 1 0 1 1 1
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| <math>(( p , q , r ))\!</math>
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|}
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<br>
    
==Venn Diagrams==
 
==Venn Diagrams==
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===New Version===
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{| align="center" cellpadding="10" style="text-align:center"
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|
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<p>[[Image:Venn Diagram (P,Q,R).jpg|500px]]</p>
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<p><math>\text{Figure 2.}~~\texttt{(p, q, r)}</math>
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|}
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{| align="center" cellpadding="10" style="text-align:center"
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|
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<p>[[Image:Venn Diagram ((P),(Q),(R)).jpg|500px]]</p>
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<p><math>\text{Figure 3.}~~\texttt{((p),(q),(r))}</math>
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|}
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===Old Version===
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{| align="center" cellpadding="10" style="text-align:center"
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|
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<p>[[Image:Minimal Negation Operator 1.jpg|500px]]</p>
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<p><math>\text{Figure 2.} ~~ \texttt{(} p \texttt{,} q \texttt{,} r \texttt{)}</math>
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|}
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{| align="center" cellpadding="10" style="text-align:center"
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|
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<p>[[Image:Minimal Negation Operator 2.jpg|500px]]</p>
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<p><math>\text{Figure 3.} ~~ \texttt{((} p \texttt{),(} q \texttt{),(} r \texttt{))}</math>
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|}
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*
Jon Awbrey
12,080

edits

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