Difference between revisions of "User:Jon Awbrey/MNO"
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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> | ||
| width="20%" | <math>\mathcal{L}_1</math> | | width="20%" | <math>\mathcal{L}_1</math> | ||
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| width="20%" | <math>\mathcal{L}_3</math> | | width="20%" | <math>\mathcal{L}_3</math> | ||
| width="20%" | <math>\mathcal{L}_4</math> | | width="20%" | <math>\mathcal{L}_4</math> | ||
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| width="20%" | <math>f_{104}\!</math> | | width="20%" | <math>f_{104}\!</math> | ||
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| <math>((p), (q), (r))\!</math> | | <math>((p), (q), (r))\!</math> | ||
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|+ <math>\text{Table A1.}~~\text{Propositional Forms on Two Variables}</math> | |+ <math>\text{Table A1.}~~\text{Propositional Forms on Two Variables}</math> | ||
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| − | | width="15%" | | + | | width="15%" | <math>\mathcal{L}_1</math> |
| − | + | | width="15%" | <math>\mathcal{L}_2</math> | |
| − | + | | width="15%" | <math>\mathcal{L}_3</math> | |
| − | | width="15%" | | + | | width="15%" | <math>\mathcal{L}_4</math> |
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Revision as of 01:40, 23 August 2009
Logical Graphs
Truth Tables
|
\(\mathcal{L}_1\) \(\text{Decimal}\) |
\(\mathcal{L}_2\) \(\text{Binary}\) |
\(\mathcal{L}_3\) \(\text{Vector}\) |
\(\mathcal{L}_4\) \(\text{Cactus}\) |
\(\mathcal{L}_5\) \(\text{English}\) |
\(\mathcal{L}_6\) \(\text{Ordinary}\) |
| \(p\colon\!\) | \(1~1~0~0\!\) | ||||
| \(q\colon\!\) | \(1~0~1~0\!\) | ||||
|
\(\begin{matrix} f_0 \\[4pt] f_1 \\[4pt] f_2 \\[4pt] f_3 \\[4pt] f_4 \\[4pt] f_5 \\[4pt] f_6 \\[4pt] f_7 \end{matrix}\) |
\(\begin{matrix} f_{0000} \\[4pt] f_{0001} \\[4pt] f_{0010} \\[4pt] f_{0011} \\[4pt] f_{0100} \\[4pt] f_{0101} \\[4pt] f_{0110} \\[4pt] f_{0111} \end{matrix}\) |
\(\begin{matrix} 0~0~0~0 \\[4pt] 0~0~0~1 \\[4pt] 0~0~1~0 \\[4pt] 0~0~1~1 \\[4pt] 0~1~0~0 \\[4pt] 0~1~0~1 \\[4pt] 0~1~1~0 \\[4pt] 0~1~1~1 \end{matrix}\) |
\(\begin{matrix} (~) \\[4pt] (p)(q) \\[4pt] (p)~q~ \\[4pt] (p)~~~ \\[4pt] ~p~(q) \\[4pt] ~~~(q) \\[4pt] (p,~q) \\[4pt] (p~~q) \end{matrix}\) |
\(\begin{matrix} \text{false} \\[4pt] \text{neither}~ p ~\text{nor}~ q \\[4pt] q ~\text{without}~ p \\[4pt] \text{not}~ p \\[4pt] p ~\text{without}~ q \\[4pt] \text{not}~ q \\[4pt] p ~\text{not equal to}~ q \\[4pt] \text{not both}~ p ~\text{and}~ q \end{matrix}\) |
\(\begin{matrix} 0 \\[4pt] \lnot p \land \lnot q \\[4pt] \lnot p \land q \\[4pt] \lnot p \\[4pt] p \land \lnot q \\[4pt] \lnot q \\[4pt] p \ne q \\[4pt] \lnot p \lor \lnot q \end{matrix}\) |
|
\(\begin{matrix} f_8 \\[4pt] f_9 \\[4pt] f_{10} \\[4pt] f_{11} \\[4pt] f_{12} \\[4pt] f_{13} \\[4pt] f_{14} \\[4pt] f_{15} \end{matrix}\) |
\(\begin{matrix} f_{1000} \\[4pt] f_{1001} \\[4pt] f_{1010} \\[4pt] f_{1011} \\[4pt] f_{1100} \\[4pt] f_{1101} \\[4pt] f_{1110} \\[4pt] f_{1111} \end{matrix}\) |
\(\begin{matrix} 1~0~0~0 \\[4pt] 1~0~0~1 \\[4pt] 1~0~1~0 \\[4pt] 1~0~1~1 \\[4pt] 1~1~0~0 \\[4pt] 1~1~0~1 \\[4pt] 1~1~1~0 \\[4pt] 1~1~1~1 \end{matrix}\) |
\(\begin{matrix} ~~p~~q~~ \\[4pt] ((p,~q)) \\[4pt] ~~~~~q~~ \\[4pt] ~(p~(q)) \\[4pt] ~~p~~~~~ \\[4pt] ((p)~q)~ \\[4pt] ((p)(q)) \\[4pt] ((~)) \end{matrix}\) |
\(\begin{matrix} p ~\text{and}~ q \\[4pt] p ~\text{equal to}~ q \\[4pt] q \\[4pt] \text{not}~ p ~\text{without}~ q \\[4pt] p \\[4pt] \text{not}~ q ~\text{without}~ p \\[4pt] p ~\text{or}~ q \\[4pt] \text{true} \end{matrix}\) |
\(\begin{matrix} p \land q \\[4pt] p = q \\[4pt] q \\[4pt] p \Rightarrow q \\[4pt] p \\[4pt] p \Leftarrow q \\[4pt] p \lor q \\[4pt] 1 \end{matrix}\) |
| \(\mathcal{L}_1\) | \(\mathcal{L}_2\) | \(\mathcal{L}_3\) | \(\mathcal{L}_4\) |
| Decimal | Binary | Sequential | Parenthetical |
| \(p =\!\) | 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 | \((( p , q , r ))\!\) |
Work Area
| \(\mathcal{L}_1\) | \(\mathcal{L}_2\) | \(\mathcal{L}_3\) | \(\mathcal{L}_4\) |
| \(p =\!\) | 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 | \((( p , q , r ))\!\) |
| \(\mathcal{L}_1\) | \(\mathcal{L}_2\) | \(\mathcal{L}_3\) | \(\mathcal{L}_4\) |
| \(p\colon\!\) | \(1~1~0~0\!\) | ||
| \(q\colon\!\) | \(1~0~1~0\!\) | ||
|
\(\begin{matrix} f_0 \\[4pt] f_1 \\[4pt] f_2 \\[4pt] f_3 \\[4pt] f_4 \\[4pt] f_5 \\[4pt] f_6 \\[4pt] f_7 \end{matrix}\) |
\(\begin{matrix} f_{0000} \\[4pt] f_{0001} \\[4pt] f_{0010} \\[4pt] f_{0011} \\[4pt] f_{0100} \\[4pt] f_{0101} \\[4pt] f_{0110} \\[4pt] f_{0111} \end{matrix}\) |
\(\begin{matrix} 0~0~0~0 \\[4pt] 0~0~0~1 \\[4pt] 0~0~1~0 \\[4pt] 0~0~1~1 \\[4pt] 0~1~0~0 \\[4pt] 0~1~0~1 \\[4pt] 0~1~1~0 \\[4pt] 0~1~1~1 \end{matrix}\) |
\(\begin{matrix} (~) \\[4pt] (p)(q) \\[4pt] (p)~q~ \\[4pt] (p)~~~ \\[4pt] ~p~(q) \\[4pt] ~~~(q) \\[4pt] (p,~q) \\[4pt] (p~~q) \end{matrix}\) |
|
\(\begin{matrix} f_8 \\[4pt] f_9 \\[4pt] f_{10} \\[4pt] f_{11} \\[4pt] f_{12} \\[4pt] f_{13} \\[4pt] f_{14} \\[4pt] f_{15} \end{matrix}\) |
\(\begin{matrix} f_{1000} \\[4pt] f_{1001} \\[4pt] f_{1010} \\[4pt] f_{1011} \\[4pt] f_{1100} \\[4pt] f_{1101} \\[4pt] f_{1110} \\[4pt] f_{1111} \end{matrix}\) |
\(\begin{matrix} 1~0~0~0 \\[4pt] 1~0~0~1 \\[4pt] 1~0~1~0 \\[4pt] 1~0~1~1 \\[4pt] 1~1~0~0 \\[4pt] 1~1~0~1 \\[4pt] 1~1~1~0 \\[4pt] 1~1~1~1 \end{matrix}\) |
\(\begin{matrix} ~~p~~q~~ \\[4pt] ((p,~q)) \\[4pt] ~~~~~q~~ \\[4pt] ~(p~(q)) \\[4pt] ~~p~~~~~ \\[4pt] ((p)~q)~ \\[4pt] ((p)(q)) \\[4pt] ((~)) \end{matrix}\) |
