| Line 171: |
Line 171: |
| | <br> | | <br> |
| | | | |
| − | {| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%" | + | {| align="center" border="1" cellpadding="6" cellspacing="0" style="text-align:center; width:90%" |
| | |+ '''Table 16. Boolean Functions on One Variable''' | | |+ '''Table 16. Boolean Functions on One Variable''' |
| | |- style="background:ghostwhite" | | |- style="background:ghostwhite" |
| Line 212: |
Line 212: |
| | <br> | | <br> |
| | | | |
| − | {| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%" | + | {| align="center" border="1" cellpadding="4" cellspacing="0" style="text-align:center; width:90%" |
| | |+ '''Table 17. Boolean Functions on Two Variables''' | | |+ '''Table 17. Boolean Functions on Two Variables''' |
| | |- style="background:ghostwhite" | | |- style="background:ghostwhite" |
| Line 355: |
Line 355: |
| | | <math>\underline{1}</math> | | | <math>\underline{1}</math> |
| | | <math>((~))</math> | | | <math>((~))</math> |
| − | |}
| |
| − |
| |
| − | <br>
| |
| − |
| |
| − | <pre>
| |
| − | Table 17. Boolean Functions on Two Variables
| |
| − | o----------o----------o-------------------------------------------o----------o
| |
| − | | Function | Function | F(x, y) | Function |
| |
| − | o----------o----------o----------o----------o----------o----------o----------o
| |
| − | | | | %1%, %1% | %1%, %0% | %0%, %1% | %0%, %0% | |
| |
| − | o----------o----------o----------o----------o----------o----------o----------o
| |
| − | | | | | | | | |
| |
| − | | F^2_00 | F^2_0000 | %0% | %0% | %0% | %0% | () |
| |
| − | | | | | | | | |
| |
| − | | F^2_01 | F^2_0001 | %0% | %0% | %0% | %1% | (x)(y) |
| |
| − | | | | | | | | |
| |
| − | | F^2_02 | F^2_0010 | %0% | %0% | %1% | %0% | (x) y |
| |
| − | | | | | | | | |
| |
| − | | F^2_03 | F^2_0011 | %0% | %0% | %1% | %1% | (x) |
| |
| − | | | | | | | | |
| |
| − | | F^2_04 | F^2_0100 | %0% | %1% | %0% | %0% | x (y) |
| |
| − | | | | | | | | |
| |
| − | | F^2_05 | F^2_0101 | %0% | %1% | %0% | %1% | (y) |
| |
| − | | | | | | | | |
| |
| − | | F^2_06 | F^2_0110 | %0% | %1% | %1% | %0% | (x, y) |
| |
| − | | | | | | | | |
| |
| − | | F^2_07 | F^2_0111 | %0% | %1% | %1% | %1% | (x y) |
| |
| − | | | | | | | | |
| |
| − | | F^2_08 | F^2_1000 | %1% | %0% | %0% | %0% | x y |
| |
| − | | | | | | | | |
| |
| − | | F^2_09 | F^2_1001 | %1% | %0% | %0% | %1% | ((x, y)) |
| |
| − | | | | | | | | |
| |
| − | | F^2_10 | F^2_1010 | %1% | %0% | %1% | %0% | y |
| |
| − | | | | | | | | |
| |
| − | | F^2_11 | F^2_1011 | %1% | %0% | %1% | %1% | (x (y)) |
| |
| − | | | | | | | | |
| |
| − | | F^2_12 | F^2_1100 | %1% | %1% | %0% | %0% | x |
| |
| − | | | | | | | | |
| |
| − | | F^2_13 | F^2_1101 | %1% | %1% | %0% | %1% | ((x) y) |
| |
| − | | | | | | | | |
| |
| − | | F^2_14 | F^2_1110 | %1% | %1% | %1% | %0% | ((x)(y)) |
| |
| − | | | | | | | | |
| |
| − | | F^2_15 | F^2_1111 | %1% | %1% | %1% | %1% | (()) |
| |
| − | | | | | | | | |
| |
| − | o----------o----------o----------o----------o----------o----------o----------o
| |
| − | </pre>
| |
| − |
| |
| − | <br>
| |
| − |
| |
| − | {| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:96%"
| |
| − | |+ '''Table 7. Propositional Forms on Two Variables'''
| |
| − | |- style="background:ghostwhite"
| |
| − | | style="width:16%" |
| |
| − | <math>\begin{matrix}\mathcal{L}_1 \\ \mbox{Decimal}\end{matrix}</math>
| |
| − | | style="width:16%" |
| |
| − | <math>\begin{matrix}\mathcal{L}_2 \\ \mbox{Binary}\end{matrix}</math>
| |
| − | | style="width:16%" |
| |
| − | <math>\begin{matrix}\mathcal{L}_3 \\ \mbox{Vector}\end{matrix}</math>
| |
| − | | style="width:16%" |
| |
| − | <math>\begin{matrix}\mathcal{L}_4 \\ \mbox{Cactus}\end{matrix}</math>
| |
| − | | style="width:16%" |
| |
| − | <math>\begin{matrix}\mathcal{L}_5 \\ \mbox{English}\end{matrix}</math>
| |
| − | | style="width:16%" |
| |
| − | <math>\begin{matrix}\mathcal{L}_6 \\ \mbox{Ordinary}\end{matrix}</math>
| |
| − | |- style="background:ghostwhite"
| |
| − | | <math>~\!</math>
| |
| − | | align="right" | <math>x\colon\!</math>
| |
| − | | <math>1~1~0~0\!</math>
| |
| − | | <math>~\!</math>
| |
| − | | <math>~\!</math>
| |
| − | | <math>~\!</math>
| |
| − | |-
| |
| − | |- style="background:ghostwhite"
| |
| − | | <math>~\!</math>
| |
| − | | align="right" | <math>y\colon\!</math>
| |
| − | | <math>1~0~1~0\!</math>
| |
| − | | <math>~\!</math>
| |
| − | | <math>~\!</math>
| |
| − | | <math>~\!</math>
| |
| − | |-
| |
| − | | <math>f_{0}\!</math>
| |
| − | | <math>f_{0000}\!</math>
| |
| − | | <math>0~0~0~0\!</math>
| |
| − | | <math>(~)\!</math>
| |
| − | | <math>\mbox{false}\!</math>
| |
| − | | <math>0\!</math>
| |
| − | |-
| |
| − | | <math>f_{1}\!</math>
| |
| − | | <math>f_{0001}\!</math>
| |
| − | | <math>0~0~0~1\!</math>
| |
| − | | <math>(x)(y)\!</math>
| |
| − | | <math>\mbox{neither}\ x\ \mbox{nor}\ y\!</math>
| |
| − | | <math>\lnot x \land \lnot y\!</math>
| |
| − | |-
| |
| − | | <math>f_{2}\!</math>
| |
| − | | <math>f_{0010}\!</math>
| |
| − | | <math>0~0~1~0\!</math>
| |
| − | | <math>(x)\ y\!</math>
| |
| − | | <math>y\ \mbox{without}\ x\!</math>
| |
| − | | <math>\lnot x \land y\!</math>
| |
| − | |-
| |
| − | | <math>f_{3}\!</math>
| |
| − | | <math>f_{0011}\!</math>
| |
| − | | <math>0~0~1~1\!</math>
| |
| − | | <math>(x)\!</math>
| |
| − | | <math>\mbox{not}\ x\!</math>
| |
| − | | <math>\lnot x\!</math>
| |
| − | |-
| |
| − | | <math>f_{4}\!</math>
| |
| − | | <math>f_{0100}\!</math>
| |
| − | | <math>0~1~0~0\!</math>
| |
| − | | <math>x\ (y)\!</math>
| |
| − | | <math>x\ \mbox{without}\ y\!</math>
| |
| − | | <math>x \land \lnot y\!</math>
| |
| − | |-
| |
| − | | <math>f_{5}\!</math>
| |
| − | | <math>f_{0101}\!</math>
| |
| − | | <math>0~1~0~1\!</math>
| |
| − | | <math>(y)\!</math>
| |
| − | | <math>\mbox{not}\ y\!</math>
| |
| − | | <math>\lnot y\!</math>
| |
| − | |-
| |
| − | | <math>f_{6}\!</math>
| |
| − | | <math>f_{0110}\!</math>
| |
| − | | <math>0~1~1~0\!</math>
| |
| − | | <math>(x, y)\!</math>
| |
| − | | <math>x\ \mbox{not equal to}\ y\!</math>
| |
| − | | <math>x \ne y\!</math>
| |
| − | |-
| |
| − | | <math>f_{7}\!</math>
| |
| − | | <math>f_{0111}\!</math>
| |
| − | | <math>0~1~1~1\!</math>
| |
| − | | <math>(x\ y)\!</math>
| |
| − | | <math>\mbox{not both}\ x\ \mbox{and}\ y\!</math>
| |
| − | | <math>\lnot x \lor \lnot y\!</math>
| |
| − | |-
| |
| − | | <math>f_{8}\!</math>
| |
| − | | <math>f_{1000}\!</math>
| |
| − | | <math>1~0~0~0\!</math>
| |
| − | | <math>x\ y\!</math>
| |
| − | | <math>x\ \mbox{and}\ y\!</math>
| |
| − | | <math>x \land y\!</math>
| |
| − | |-
| |
| − | | <math>f_{9}\!</math>
| |
| − | | <math>f_{1001}\!</math>
| |
| − | | <math>1~0~0~1\!</math>
| |
| − | | <math>((x, y))\!</math>
| |
| − | | <math>x\ \mbox{equal to}\ y\!</math>
| |
| − | | <math>x = y\!</math>
| |
| − | |-
| |
| − | | <math>f_{10}\!</math>
| |
| − | | <math>f_{1010}\!</math>
| |
| − | | <math>1~0~1~0\!</math>
| |
| − | | <math>y\!</math>
| |
| − | | <math>y\!</math>
| |
| − | | <math>y\!</math>
| |
| − | |-
| |
| − | | <math>f_{11}\!</math>
| |
| − | | <math>f_{1011}\!</math>
| |
| − | | <math>1~0~1~1\!</math>
| |
| − | | <math>(x\ (y))\!</math>
| |
| − | | <math>\mbox{not}\ x\ \mbox{without}\ y\!</math>
| |
| − | | <math>x \Rightarrow y\!</math>
| |
| − | |-
| |
| − | | <math>f_{12}\!</math>
| |
| − | | <math>f_{1100}\!</math>
| |
| − | | <math>1~1~0~0\!</math>
| |
| − | | <math>x\!</math>
| |
| − | | <math>x\!</math>
| |
| − | | <math>x\!</math>
| |
| − | |-
| |
| − | | <math>f_{13}\!</math>
| |
| − | | <math>f_{1101}\!</math>
| |
| − | | <math>1~1~0~1\!</math>
| |
| − | | <math>((x)\ y)\!</math>
| |
| − | | <math>\mbox{not}\ y\ \mbox{without}\ x\!</math>
| |
| − | | <math>x \Leftarrow y\!</math>
| |
| − | |-
| |
| − | | <math>f_{14}\!</math>
| |
| − | | <math>f_{1110}\!</math>
| |
| − | | <math>1~1~1~0\!</math>
| |
| − | | <math>((x)(y))\!</math>
| |
| − | | <math>x\ \mbox{or}\ y\!</math>
| |
| − | | <math>x \lor y\!</math>
| |
| − | |-
| |
| − | | <math>f_{15}\!</math>
| |
| − | | <math>f_{1111}\!</math>
| |
| − | | <math>1~1~1~1\!</math>
| |
| − | | <math>((~))\!</math>
| |
| − | | <math>\mbox{true}\!</math>
| |
| − | | <math>1\!</math>
| |
| | |} | | |} |
| | | | |