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MyWikiBiz, Author Your Legacy — Sunday February 16, 2025
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| 1 0 0 1 0 1 1 1
| 1 0 0 1 0 1 1 1
| <math>(( p , q , r ))\!</math>
| <math>(( p , q , r ))\!</math>
|}
<br>
==Work Area==
<br>
{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:#f0f0ff; font-weight:bold; text-align:center; width:80%"
|+ <math>\text{Table 1.}~~\text{Logical Boundaries and Their Complements}</math>
| width="20%" | <math>\mathcal{L}_1</math>
| width="20%" | <math>\mathcal{L}_2</math>
| width="20%" | <math>\mathcal{L}_3</math>
| width="20%" | <math>\mathcal{L}_4</math>
|-
| Decimal
| Binary
| Sequential
| Parenthetical
|-
|
| align="right" | <math>p =\!</math>
| 1 1 1 1 0 0 0 0
|
|-
|
| align="right" | <math>q =\!</math>
| 1 1 0 0 1 1 0 0
|
|-
|
| align="right" | <math>r =\!</math>
| 1 0 1 0 1 0 1 0
|
|}
{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:ghostwhite; font-weight:bold; text-align:center; width:80%"
|-
| width="20%" | <math>f_{104}\!</math>
| width="20%" | <math>f_{01101000}\!</math>
| width="20%" | 0 1 1 0 1 0 0 0
| width="20%" | <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="background:ghostwhite; font-weight:bold; text-align:center; width:80%"
|-
| width="20%" | <math>f_{233}\!</math>
| width="20%" | <math>f_{11101001}\!</math>
| width="20%" | 1 1 1 0 1 0 0 1
| width="20%" | <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>
{| 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>
|- style="background:#f0f0ff"
| width="15%" |
<p><math>\mathcal{L}_1</math></p>
<p><math>\text{Decimal}</math></p>
| width="15%" |
<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"
|
| align="right" | <math>p\colon\!</math>
| <math>1~1~0~0\!</math>
|
|
|
|- style="background:#f0f0ff"
|
| align="right" | <math>q\colon\!</math>
| <math>1~0~1~0\!</math>
|
|
|
|-
|
<math>\begin{matrix}
f_0
\\[4pt]
f_1
\\[4pt]
f_2
\\[4pt]
f_3
\\[4pt]
f_4
\\[4pt]
f_5
\\[4pt]
f_6
\\[4pt]
f_7
\end{matrix}</math>
|
<math>\begin{matrix}
f_{0000}
\\[4pt]
f_{0001}
\\[4pt]
f_{0010}
\\[4pt]
f_{0011}
\\[4pt]
f_{0100}
\\[4pt]
f_{0101}
\\[4pt]
f_{0110}
\\[4pt]
f_{0111}
\end{matrix}</math>
|
<math>\begin{matrix}
0~0~0~0
\\[4pt]
0~0~0~1
\\[4pt]
0~0~1~0
\\[4pt]
0~0~1~1
\\[4pt]
0~1~0~0
\\[4pt]
0~1~0~1
\\[4pt]
0~1~1~0
\\[4pt]
0~1~1~1
\end{matrix}</math>
|
<math>\begin{matrix}
(~)
\\[4pt]
(p)(q)
\\[4pt]
(p)~q~
\\[4pt]
(p)~~~
\\[4pt]
~p~(q)
\\[4pt]
~~~(q)
\\[4pt]
(p,~q)
\\[4pt]
(p~~q)
\end{matrix}</math>
|
<math>\begin{matrix}
\text{false}
\\[4pt]
\text{neither}~ p ~\text{nor}~ q
\\[4pt]
q ~\text{without}~ p
\\[4pt]
\text{not}~ p
\\[4pt]
p ~\text{without}~ q
\\[4pt]
\text{not}~ q
\\[4pt]
p ~\text{not equal to}~ q
\\[4pt]
\text{not both}~ p ~\text{and}~ q
\end{matrix}</math>
|
<math>\begin{matrix}
0
\\[4pt]
\lnot p \land \lnot q
\\[4pt]
\lnot p \land q
\\[4pt]
\lnot p
\\[4pt]
p \land \lnot q
\\[4pt]
\lnot q
\\[4pt]
p \ne q
\\[4pt]
\lnot p \lor \lnot q
\end{matrix}</math>
|-
|
<math>\begin{matrix}
f_8
\\[4pt]
f_9
\\[4pt]
f_{10}
\\[4pt]
f_{11}
\\[4pt]
f_{12}
\\[4pt]
f_{13}
\\[4pt]
f_{14}
\\[4pt]
f_{15}
\end{matrix}</math>
|
<math>\begin{matrix}
f_{1000}
\\[4pt]
f_{1001}
\\[4pt]
f_{1010}
\\[4pt]
f_{1011}
\\[4pt]
f_{1100}
\\[4pt]
f_{1101}
\\[4pt]
f_{1110}
\\[4pt]
f_{1111}
\end{matrix}</math>
|
<math>\begin{matrix}
1~0~0~0
\\[4pt]
1~0~0~1
\\[4pt]
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~~q~~
\\[4pt]
((p,~q))
\\[4pt]
~~~~~q~~
\\[4pt]
~(p~(q))
\\[4pt]
~~p~~~~~
\\[4pt]
((p)~q)~
\\[4pt]
((p)(q))
\\[4pt]
((~))
\end{matrix}</math>
|
<math>\begin{matrix}
p ~\text{and}~ q
\\[4pt]
p ~\text{equal to}~ q
\\[4pt]
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 \land q
\\[4pt]
p = q
\\[4pt]
q
\\[4pt]
p \Rightarrow q
\\[4pt]
p
\\[4pt]
p \Leftarrow q
\\[4pt]
p \lor q
\\[4pt]
1
\end{matrix}</math>
|}
|}
