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" |
| | | | | |
| | 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> |
− | |
| |
− | |
| |
| | | | | |
| |- style="background:#f0f0ff" | | |- style="background:#f0f0ff" |
| | | | | |
| | 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> |
| | | | | |
| + | |- style="background:#f0f0ff" |
| | | | | |
| + | | align="right" | <math>r\colon\!</math> |
| + | | <math>1~0~1~0~1~0~1~0</math> |
| | | | | |
| |- | | |- |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | f_0
| + | f_{104} |
− | \\[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] | | \\[4pt] |
− | f_{0001} | + | f_{148} |
| \\[4pt] | | \\[4pt] |
− | f_{0010} | + | f_{146} |
| \\[4pt] | | \\[4pt] |
− | f_{0011} | + | f_{97} |
| \\[4pt] | | \\[4pt] |
− | f_{0100} | + | f_{134} |
| \\[4pt] | | \\[4pt] |
− | f_{0101} | + | f_{73} |
| \\[4pt] | | \\[4pt] |
− | f_{0110} | + | f_{41} |
| \\[4pt] | | \\[4pt] |
− | f_{0111} | + | f_{22} |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | 0~0~0~0
| + | f_{01101000} |
| \\[4pt] | | \\[4pt] |
− | 0~0~0~1
| + | f_{10010100} |
| \\[4pt] | | \\[4pt] |
− | 0~0~1~0
| + | f_{10010010} |
| \\[4pt] | | \\[4pt] |
− | 0~0~1~1
| + | f_{01100001} |
| \\[4pt] | | \\[4pt] |
− | 0~1~0~0
| + | f_{10000110} |
| \\[4pt] | | \\[4pt] |
− | 0~1~0~1
| + | f_{01001001} |
| \\[4pt] | | \\[4pt] |
− | 0~1~1~0
| + | f_{00101001} |
| \\[4pt] | | \\[4pt] |
− | 0~1~1~1
| + | f_{00010110} |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | (~)
| + | 0~1~1~0~1~0~0~0 |
| \\[4pt] | | \\[4pt] |
− | (p)(q)
| + | 1~0~0~1~0~1~0~0 |
| \\[4pt] | | \\[4pt] |
− | (p)~q~
| + | 1~0~0~1~0~0~1~0 |
| \\[4pt] | | \\[4pt] |
− | (p)~~~
| + | 0~1~1~0~0~0~0~1 |
| \\[4pt] | | \\[4pt] |
− | ~p~(q) | + | 1~0~0~0~0~1~1~0 |
| \\[4pt] | | \\[4pt] |
− | ~~~(q) | + | 0~1~0~0~1~0~0~1 |
| \\[4pt] | | \\[4pt] |
− | (p,~q)
| + | 0~0~1~0~1~0~0~1 |
| \\[4pt] | | \\[4pt] |
− | (p~~q)
| + | 0~0~0~1~0~1~1~0 |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | \text{false} | + | \texttt{(~p~,~q~,~r~)} |
| \\[4pt] | | \\[4pt] |
− | \text{neither}~ p ~\text{nor}~ q | + | \texttt{(~p~,~q~,(r))} |
| \\[4pt] | | \\[4pt] |
− | q ~\text{without}~ p
| + | \texttt{(~p~,(q),~r~)} |
| \\[4pt] | | \\[4pt] |
− | \text{not}~ p | + | \texttt{(~p~,(q),(r))} |
| \\[4pt] | | \\[4pt] |
− | p ~\text{without}~ q
| + | \texttt{((p),~q~,~r~)} |
| \\[4pt] | | \\[4pt] |
− | \text{not}~ q | + | \texttt{((p),~q~,(r))} |
| \\[4pt] | | \\[4pt] |
− | p ~\text{not equal to}~ q | + | \texttt{((p),(q),~r~)} |
| \\[4pt] | | \\[4pt] |
− | \text{not both}~ p ~\text{and}~ q | + | \texttt{((p),(q),(r))} |
− | \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> | | \end{matrix}</math> |
| |- | | |- |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | f_8
| + | f_{233} |
| \\[4pt] | | \\[4pt] |
− | f_9
| + | f_{214} |
| \\[4pt] | | \\[4pt] |
− | f_{10} | + | f_{182} |
| \\[4pt] | | \\[4pt] |
− | f_{11} | + | f_{121} |
| \\[4pt] | | \\[4pt] |
− | f_{12} | + | f_{158} |
| \\[4pt] | | \\[4pt] |
− | f_{13} | + | f_{109} |
| \\[4pt] | | \\[4pt] |
− | f_{14} | + | f_{107} |
| \\[4pt] | | \\[4pt] |
− | f_{15} | + | f_{151} |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | f_{1000} | + | f_{11101001} |
| \\[4pt] | | \\[4pt] |
− | f_{1001} | + | f_{11010110} |
| \\[4pt] | | \\[4pt] |
− | f_{1010} | + | f_{10110110} |
| \\[4pt] | | \\[4pt] |
− | f_{1011} | + | f_{01111001} |
| \\[4pt] | | \\[4pt] |
− | f_{1100} | + | f_{10011110} |
| \\[4pt] | | \\[4pt] |
− | f_{1101} | + | f_{01101101} |
| \\[4pt] | | \\[4pt] |
− | f_{1110} | + | f_{01101011} |
| \\[4pt] | | \\[4pt] |
− | f_{1111} | + | f_{10010111} |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | 1~0~0~0 | + | 1~1~1~0~1~0~0~1 |
| \\[4pt] | | \\[4pt] |
− | 1~0~0~1 | + | 1~1~0~1~0~1~1~0 |
| \\[4pt] | | \\[4pt] |
− | 1~0~1~0 | + | 1~0~1~1~0~1~1~0 |
| \\[4pt] | | \\[4pt] |
− | 1~0~1~1 | + | 0~1~1~1~1~0~0~1 |
| \\[4pt] | | \\[4pt] |
− | 1~1~0~0 | + | 1~0~0~1~1~1~1~0 |
| \\[4pt] | | \\[4pt] |
− | 1~1~0~1 | + | 0~1~1~0~1~1~0~1 |
| \\[4pt] | | \\[4pt] |
− | 1~1~1~0 | + | 0~1~1~0~1~0~1~1 |
| \\[4pt] | | \\[4pt] |
− | 1~1~1~1 | + | 1~0~0~1~0~1~1~1 |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | ~~p~~q~~
| + | \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~~~~~
| + | \texttt{((~p~,(q),(r)))} |
| \\[4pt] | | \\[4pt] |
− | ((p)~q)~ | + | \texttt{((~p~,(q),~r~))} |
| \\[4pt] | | \\[4pt] |
− | ((p)(q)) | + | \texttt{((~p~,~q~,(r)))} |
| \\[4pt] | | \\[4pt] |
− | ((~)) | + | \texttt{((~p~,~q~,~r~))} |
− | \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> | | \end{matrix}</math> |
| |} | | |} |
Line 262: |
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| <br> | | <br> |
| | | |
− | {| align="center" border="1" cellpadding="4" cellspacing="0" style="background:#f0f0ff; font-weight:bold; text-align:center; width:80%"
| + | ===Old Version=== |
− | |+ <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>
| |
− | | |
− | ==Work Area==
| |
| | | |
| <br> | | <br> |
Line 382: |
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| {| align="center" border="1" cellpadding="4" cellspacing="0" style="background:#f0f0ff; font-weight:bold; text-align:center; width:90%" | | {| 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> | | |+ <math>\text{Table 1.}~~\text{Logical Boundaries and Their Complements}</math> |
− | | width="20%" | <math>\mathcal{L}_1</math> | + | | width="25%" | <math>\mathcal{L}_1</math> |
− | | width="20%" | <math>\mathcal{L}_2</math> | + | | width="25%" | <math>\mathcal{L}_2</math> |
− | | width="20%" | <math>\mathcal{L}_3</math> | + | | width="25%" | <math>\mathcal{L}_3</math> |
− | | width="20%" | <math>\mathcal{L}_4</math> | + | | width="25%" | <math>\mathcal{L}_4</math> |
| |- | | |- |
| | | | | |
Line 404: |
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| {| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:90%" | | {| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:90%" |
| |- | | |- |
− | | width="20%" | <math>f_{104}\!</math> | + | | width="25%" | <math>f_{104}\!</math> |
− | | width="20%" | <math>f_{01101000}\!</math> | + | | width="25%" | <math>f_{01101000}\!</math> |
− | | width="20%" | 0 1 1 0 1 0 0 0 | + | | width="25%" | 0 1 1 0 1 0 0 0 |
− | | width="20%" | <math>( p , q , r )\!</math> | + | | width="25%" | <math>( p , q , r )\!</math> |
| |- | | |- |
| | <math>f_{148}\!</math> | | | <math>f_{148}\!</math> |
Line 446: |
Line 249: |
| {| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:90%" | | {| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:90%" |
| |- | | |- |
− | | width="20%" | <math>f_{233}\!</math> | + | | width="25%" | <math>f_{233}\!</math> |
− | | width="20%" | <math>f_{11101001}\!</math> | + | | width="25%" | <math>f_{11101001}\!</math> |
− | | width="20%" | 1 1 1 0 1 0 0 1 | + | | width="25%" | 1 1 1 0 1 0 0 1 |
− | | width="20%" | <math>(((p), (q), (r)))\!</math> | + | | width="25%" | <math>(((p), (q), (r)))\!</math> |
| |- | | |- |
| | <math>f_{214}\!</math> | | | <math>f_{214}\!</math> |
Line 489: |
Line 292: |
| <br> | | <br> |
| | | |
− | {| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%"
| + | ==Venn Diagrams== |
− | |+ <math>\text{Table A1.}~~\text{Propositional Forms on Two Variables}</math>
| + | |
− | |- style="background:#f0f0ff"
| + | ===New Version=== |
− | | width="15%" | <math>\mathcal{L}_1</math>
| + | |
− | | width="15%" | <math>\mathcal{L}_2</math>
| + | {| align="center" cellpadding="10" style="text-align:center" |
− | | width="15%" | <math>\mathcal{L}_3</math>
| |
− | | width="15%" | <math>\mathcal{L}_4</math>
| |
− | |- 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} | + | <p>[[Image:Venn Diagram (P,Q,R).jpg|500px]]</p> |
− | f_0
| + | <p><math>\text{Figure 2.}~~\texttt{(p, q, r)}</math> |
− | \\[4pt]
| + | |} |
− | f_1
| + | |
− | \\[4pt]
| + | {| align="center" cellpadding="10" style="text-align:center" |
− | f_2
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− | \\[4pt]
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− | f_3
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− | \\[4pt] | |
− | f_4
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− | \\[4pt]
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− | f_5
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− | \\[4pt]
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− | f_6
| |
− | \\[4pt]
| |
− | f_7
| |
− | \end{matrix}</math>
| |
| | | | | |
− | <math>\begin{matrix} | + | <p>[[Image:Venn Diagram ((P),(Q),(R)).jpg|500px]]</p> |
− | f_{0000}
| + | <p><math>\text{Figure 3.}~~\texttt{((p),(q),(r))}</math> |
− | \\[4pt]
| + | |} |
− | f_{0001}
| + | |
− | \\[4pt]
| + | ===Old Version=== |
− | f_{0010}
| + | |
− | \\[4pt]
| + | {| align="center" cellpadding="10" style="text-align:center" |
− | f_{0011}
| |
− | \\[4pt] | |
− | f_{0100}
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− | \\[4pt]
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− | f_{0101}
| |
− | \\[4pt]
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− | f_{0110}
| |
− | \\[4pt]
| |
− | f_{0111}
| |
− | \end{matrix}</math>
| |
| | | | | |
− | <math>\begin{matrix} | + | <p>[[Image:Minimal Negation Operator 1.jpg|500px]]</p> |
− | 0~0~0~0
| + | <p><math>\text{Figure 2.} ~~ \texttt{(} p \texttt{,} q \texttt{,} r \texttt{)}</math> |
− | \\[4pt]
| + | |} |
− | 0~0~0~1
| + | |
− | \\[4pt]
| + | {| align="center" cellpadding="10" style="text-align:center" |
− | 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} | |
− | 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>[[Image:Minimal Negation Operator 2.jpg|500px]]</p> |
− | ~~p~~q~~
| + | <p><math>\text{Figure 3.} ~~ \texttt{((} p \texttt{),(} q \texttt{),(} r \texttt{))}</math> |
− | \\[4pt]
| |
− | ((p,~q))
| |
− | \\[4pt]
| |
− | ~~~~~q~~
| |
− | \\[4pt]
| |
− | ~(p~(q))
| |
− | \\[4pt] | |
− | ~~p~~~~~
| |
− | \\[4pt] | |
− | ((p)~q)~ | |
− | \\[4pt] | |
− | ((p)(q))
| |
− | \\[4pt] | |
− | ((~))
| |
− | \end{matrix}</math>
| |
| |} | | |} |
| | | |
− | <br>
| + | * |
− | | |
− | ==Venn Diagrams==
| |