Line 3,090: |
Line 3,090: |
| | <math>f_{0000}\!</math> | | | <math>f_{0000}\!</math> |
| | 0 0 0 0 | | | 0 0 0 0 |
− | | <math>(\!|~|\!)</math> | + | | <math>(~)\!</math> |
| | false | | | false |
| | <math>0\!</math> | | | <math>0\!</math> |
Line 3,097: |
Line 3,097: |
| | <math>f_{0001}\!</math> | | | <math>f_{0001}\!</math> |
| | 0 0 0 1 | | | 0 0 0 1 |
− | | <math>(\!|x|\!)(\!|y|\!)</math> | + | | <math>(x)(y)\!</math> |
| | neither x nor y | | | neither x nor y |
− | | <math>\lnot x \land \lnot y</math> | + | | <math>\lnot x \land \lnot y\!</math> |
| |- | | |- |
| | <math>f_{2}\!</math> | | | <math>f_{2}\!</math> |
| | <math>f_{0010}\!</math> | | | <math>f_{0010}\!</math> |
| | 0 0 1 0 | | | 0 0 1 0 |
− | | <math>(\!|x|\!)\ y</math> | + | | <math>(x)\ y\!</math> |
| | y and not x | | | y and not x |
− | | <math>\lnot x \land y</math> | + | | <math>\lnot x \land y\!</math> |
| |- | | |- |
| | <math>f_{3}\!</math> | | | <math>f_{3}\!</math> |
| | <math>f_{0011}\!</math> | | | <math>f_{0011}\!</math> |
| | 0 0 1 1 | | | 0 0 1 1 |
− | | <math>(\!|x|\!)</math> | + | | <math>(x)\!</math> |
| | not x | | | not x |
− | | <math>\lnot x</math> | + | | <math>\lnot x\!</math> |
| |- | | |- |
| | <math>f_{4}\!</math> | | | <math>f_{4}\!</math> |
| | <math>f_{0100}\!</math> | | | <math>f_{0100}\!</math> |
| | 0 1 0 0 | | | 0 1 0 0 |
− | | <math>x\ (\!|y|\!)</math> | + | | <math>x\ (y)\!</math> |
| | x and not y | | | x and not y |
− | | <math>x \land \lnot y</math> | + | | <math>x \land \lnot y\!</math> |
| |- | | |- |
| | <math>f_{5}\!</math> | | | <math>f_{5}\!</math> |
| | <math>f_{0101}\!</math> | | | <math>f_{0101}\!</math> |
| | 0 1 0 1 | | | 0 1 0 1 |
− | | <math>(\!|y|\!)</math> | + | | <math>(y)\!</math> |
| | not y | | | not y |
− | | <math>\lnot y</math> | + | | <math>\lnot y\!</math> |
| |- | | |- |
| | <math>f_{6}\!</math> | | | <math>f_{6}\!</math> |
| | <math>f_{0110}\!</math> | | | <math>f_{0110}\!</math> |
| | 0 1 1 0 | | | 0 1 1 0 |
− | | <math>(\!|x,\ y|\!)</math> | + | | <math>(x,\ y)\!</math> |
| | x not equal to y | | | x not equal to y |
− | | <math>x \ne y</math> | + | | <math>x \ne y\!</math> |
| |- | | |- |
| | <math>f_{7}\!</math> | | | <math>f_{7}\!</math> |
| | <math>f_{0111}\!</math> | | | <math>f_{0111}\!</math> |
| | 0 1 1 1 | | | 0 1 1 1 |
− | | <math>(\!|x\ y|\!)</math> | + | | <math>(x\ y)\!</math> |
| | not both x and y | | | not both x and y |
− | | <math>\lnot x \lor \lnot y</math> | + | | <math>\lnot x \lor \lnot y\!</math> |
| |- | | |- |
| | <math>f_{8}\!</math> | | | <math>f_{8}\!</math> |
| | <math>f_{1000}\!</math> | | | <math>f_{1000}\!</math> |
| | 1 0 0 0 | | | 1 0 0 0 |
− | | <math>x\ y</math> | + | | <math>x\ y\!</math> |
| | x and y | | | x and y |
− | | <math>x \land y</math> | + | | <math>x \land y\!</math> |
| |- | | |- |
| | <math>f_{9}\!</math> | | | <math>f_{9}\!</math> |
| | <math>f_{1001}\!</math> | | | <math>f_{1001}\!</math> |
| | 1 0 0 1 | | | 1 0 0 1 |
− | | <math>(\!|(\!|x,\ y|\!)|\!)</math> | + | | <math>((x,\ y))\!</math> |
| | x equal to y | | | x equal to y |
| | <math>x = y\!</math> | | | <math>x = y\!</math> |
Line 3,167: |
Line 3,167: |
| | <math>f_{1011}\!</math> | | | <math>f_{1011}\!</math> |
| | 1 0 1 1 | | | 1 0 1 1 |
− | | <math>(\!|x\ (\!|y|\!)|\!)</math> | + | | <math>(x\ (y))\!</math> |
| | not x without y | | | not x without y |
− | | <math>x \Rightarrow y</math> | + | | <math>x \Rightarrow y\!</math> |
| |- | | |- |
| | <math>f_{12}\!</math> | | | <math>f_{12}\!</math> |
Line 3,181: |
Line 3,181: |
| | <math>f_{1101}\!</math> | | | <math>f_{1101}\!</math> |
| | 1 1 0 1 | | | 1 1 0 1 |
− | | <math>(\!|(\!|x|\!)\ y|\!)</math> | + | | <math>((x)\ y)\!</math> |
| | not y without x | | | not y without x |
− | | <math>x \Leftarrow y</math> | + | | <math>x \Leftarrow y\!</math> |
| |- | | |- |
| | <math>f_{14}\!</math> | | | <math>f_{14}\!</math> |
| | <math>f_{1110}\!</math> | | | <math>f_{1110}\!</math> |
| | 1 1 1 0 | | | 1 1 1 0 |
− | | <math>(\!|(\!|x|\!)(\!|y|\!)|\!)</math> | + | | <math>((x)(y))\!</math> |
| | x or y | | | x or y |
− | | <math>x \lor y</math> | + | | <math>x \lor y\!</math> |
| |- | | |- |
| | <math>f_{15}\!</math> | | | <math>f_{15}\!</math> |
| | <math>f_{1111}\!</math> | | | <math>f_{1111}\!</math> |
| | 1 1 1 1 | | | 1 1 1 1 |
− | | <math>(\!|(\!|~|\!)|\!)</math> | + | | <math>((~))\!</math> |
| | true | | | true |
| | <math>1\!</math> | | | <math>1\!</math> |
Line 3,207: |
Line 3,207: |
| | style="width:16%" | | | | style="width:16%" | |
| | style="width:16%" | <math>f\!</math> | | | style="width:16%" | <math>f\!</math> |
− | | style="width:16%" | <math>\operatorname{E}f|_{xy}</math> | + | | style="width:16%" | <math>\operatorname{E}f|_{xy}\!</math> |
− | | style="width:16%" | <math>\operatorname{E}f|_{x(\!|y|\!)}</math> | + | | style="width:16%" | <math>\operatorname{E}f|_{x(y)}\!</math> |
− | | style="width:16%" | <math>\operatorname{E}f|_{(\!|x|\!)y}</math> | + | | style="width:16%" | <math>\operatorname{E}f|_{(x)y}\!</math> |
− | | style="width:16%" | <math>\operatorname{E}f|_{(\!|x|\!)(\!|y|\!)}</math> | + | | style="width:16%" | <math>\operatorname{E}f|_{(x)(y)}\!</math> |
| |- | | |- |
| | <math>f_{0}\!</math> | | | <math>f_{0}\!</math> |
− | | <math>(\!|~|\!)</math> | + | | <math>(~)\!</math> |
− | | <math>(\!|~|\!)</math> | + | | <math>(~)\!</math> |
− | | <math>(\!|~|\!)</math> | + | | <math>(~)\!</math> |
− | | <math>(\!|~|\!)</math> | + | | <math>(~)\!</math> |
− | | <math>(\!|~|\!)</math> | + | | <math>(~)\!</math> |
| |- | | |- |
| | <math>f_{1}\!</math> | | | <math>f_{1}\!</math> |
− | | <math>(\!|x|\!)(\!|y|\!)</math> | + | | <math>(x)(y)\!</math> |
− | | <math>\operatorname{d}x\ \operatorname{d}y</math> | + | | <math>\operatorname{d}x\ \operatorname{d}y\!</math> |
− | | <math>\operatorname{d}x (\!|\operatorname{d}y|\!)</math> | + | | <math>\operatorname{d}x (\operatorname{d}y)\!</math> |
− | | <math>(\!|\operatorname{d}x|\!) \operatorname{d}y</math> | + | | <math>(\operatorname{d}x) \operatorname{d}y\!</math> |
− | | <math>(\!|\operatorname{d}x|\!)(\!|\operatorname{d}y|\!)</math> | + | | <math>(\operatorname{d}x)(\operatorname{d}y)\!</math> |
| |- | | |- |
| | <math>f_{2}\!</math> | | | <math>f_{2}\!</math> |
− | | <math>(\!|x|\!) y</math> | + | | <math>(x) y\!</math> |
− | | <math>\operatorname{d}x (\!|\operatorname{d}y|\!)</math> | + | | <math>\operatorname{d}x (\operatorname{d}y)\!</math> |
− | | <math>\operatorname{d}x\ \operatorname{d}y</math> | + | | <math>\operatorname{d}x\ \operatorname{d}y\!</math> |
− | | <math>(\!|\operatorname{d}x|\!)(\!|\operatorname{d}y|\!)</math> | + | | <math>(\operatorname{d}x)(\operatorname{d}y)\!</math> |
− | | <math>(\!|\operatorname{d}x|\!) \operatorname{d}y</math> | + | | <math>(\operatorname{d}x) \operatorname{d}y\!</math> |
| |- | | |- |
| | <math>f_{4}\!</math> | | | <math>f_{4}\!</math> |
− | | <math>x (\!|y|\!)</math> | + | | <math>x (y)\!</math> |
− | | <math>(\!|\operatorname{d}x|\!) \operatorname{d}y</math> | + | | <math>(\operatorname{d}x) \operatorname{d}y\!</math> |
− | | <math>(\!|\operatorname{d}x|\!)(\!|\operatorname{d}y|\!)</math> | + | | <math>(\operatorname{d}x)(\operatorname{d}y)\!</math> |
− | | <math>\operatorname{d}x\ \operatorname{d}y</math> | + | | <math>\operatorname{d}x\ \operatorname{d}y\!</math> |
− | | <math>\operatorname{d}x (\!|\operatorname{d}y|\!)</math> | + | | <math>\operatorname{d}x (\operatorname{d}y)\!</math> |
| |- | | |- |
| | <math>f_{8}\!</math> | | | <math>f_{8}\!</math> |
| | <math>x y\!</math> | | | <math>x y\!</math> |
− | | <math>(\!|\operatorname{d}x|\!)(\!|\operatorname{d}y|\!)</math> | + | | <math>(\operatorname{d}x)(\operatorname{d}y)\!</math> |
− | | <math>(\!|\operatorname{d}x|\!) \operatorname{d}y</math> | + | | <math>(\operatorname{d}x) \operatorname{d}y\!</math> |
− | | <math>\operatorname{d}x (\!|\operatorname{d}y|\!)</math> | + | | <math>\operatorname{d}x (\operatorname{d}y)\!</math> |
− | | <math>\operatorname{d}x\ \operatorname{d}y</math> | + | | <math>\operatorname{d}x\ \operatorname{d}y\!</math> |
| |- | | |- |
| | <math>f_{3}\!</math> | | | <math>f_{3}\!</math> |
− | | <math>(\!|x|\!)</math> | + | | <math>(x)\!</math> |
− | | <math>\operatorname{d}x</math> | + | | <math>\operatorname{d}x\!</math> |
− | | <math>\operatorname{d}x</math> | + | | <math>\operatorname{d}x\!</math> |
− | | <math>(\!|\operatorname{d}x|\!)</math> | + | | <math>(\operatorname{d}x)\!</math> |
− | | <math>(\!|\operatorname{d}x|\!)</math> | + | | <math>(\operatorname{d}x)\!</math> |
| |- | | |- |
| | <math>f_{12}\!</math> | | | <math>f_{12}\!</math> |
| | <math>x\!</math> | | | <math>x\!</math> |
− | | <math>(\!|\operatorname{d}x|\!)</math> | + | | <math>(\operatorname{d}x)\!</math> |
− | | <math>(\!|\operatorname{d}x|\!)</math> | + | | <math>(\operatorname{d}x)\!</math> |
− | | <math>\operatorname{d}x</math> | + | | <math>\operatorname{d}x\!</math> |
− | | <math>\operatorname{d}x</math> | + | | <math>\operatorname{d}x\!</math> |
| |- | | |- |
| | <math>f_{6}\!</math> | | | <math>f_{6}\!</math> |
− | | <math>(\!|x, y|\!)</math> | + | | <math>(x, y)\!</math> |
− | | <math>(\!|\operatorname{d}x, \operatorname{d}y|\!)</math> | + | | <math>(\operatorname{d}x, \operatorname{d}y)\!</math> |
− | | <math>(\!|(\!|\operatorname{d}x, \operatorname{d}y|\!)|\!)</math> | + | | <math>((\operatorname{d}x, \operatorname{d}y))\!</math> |
− | | <math>(\!|(\!|\operatorname{d}x, \operatorname{d}y|\!)|\!)</math> | + | | <math>((\operatorname{d}x, \operatorname{d}y))\!</math> |
− | | <math>(\!|\operatorname{d}x, \operatorname{d}y|\!)</math> | + | | <math>(\operatorname{d}x, \operatorname{d}y)\!</math> |
| |- | | |- |
| | <math>f_{9}\!</math> | | | <math>f_{9}\!</math> |
− | | <math>(\!|(\!|x, y|\!)|\!)</math> | + | | <math>((x, y))\!</math> |
− | | <math>(\!|(\!|\operatorname{d}x, \operatorname{d}y|\!)|\!)</math> | + | | <math>((\operatorname{d}x, \operatorname{d}y))\!</math> |
− | | <math>(\!|\operatorname{d}x, \operatorname{d}y|\!)</math> | + | | <math>(\operatorname{d}x, \operatorname{d}y)\!</math> |
− | | <math>(\!|\operatorname{d}x, \operatorname{d}y|\!)</math> | + | | <math>(\operatorname{d}x, \operatorname{d}y)\!</math> |
− | | <math>(\!|(\!|\operatorname{d}x, \operatorname{d}y|\!)|\!)</math> | + | | <math>((\operatorname{d}x, \operatorname{d}y))\!</math> |
| |- | | |- |
| | <math>f_{5}\!</math> | | | <math>f_{5}\!</math> |
− | | <math>(\!|y|\!)</math> | + | | <math>(y)\!</math> |
− | | <math>\operatorname{d}y</math> | + | | <math>\operatorname{d}y\!</math> |
− | | <math>(\!|\operatorname{d}y|\!)</math> | + | | <math>(\operatorname{d}y)\!</math> |
− | | <math>\operatorname{d}y</math> | + | | <math>\operatorname{d}y\!</math> |
− | | <math>(\!|\operatorname{d}y|\!)</math> | + | | <math>(\operatorname{d}y)\!</math> |
| |- | | |- |
| | <math>f_{10}\!</math> | | | <math>f_{10}\!</math> |
| | <math>y\!</math> | | | <math>y\!</math> |
− | | <math>(\!|\operatorname{d}y|\!)</math> | + | | <math>(\operatorname{d}y)\!</math> |
− | | <math>\operatorname{d}y</math> | + | | <math>\operatorname{d}y\!</math> |
− | | <math>(\!|\operatorname{d}y|\!)</math> | + | | <math>(\operatorname{d}y)\!</math> |
− | | <math>\operatorname{d}y</math> | + | | <math>\operatorname{d}y\!</math> |
| |- | | |- |
| | <math>f_{7}\!</math> | | | <math>f_{7}\!</math> |
− | | <math>(\!|x y|\!)</math> | + | | <math>(x y)\!</math> |
− | | <math>(\!|(\!|\operatorname{d}x|\!)(\!|\operatorname{d}y|\!)|\!)</math> | + | | <math>((\operatorname{d}x)(\operatorname{d}y))\!</math> |
− | | <math>(\!|(\!|\operatorname{d}x|\!) \operatorname{d}y|\!)</math> | + | | <math>((\operatorname{d}x) \operatorname{d}y)\!</math> |
− | | <math>(\!|\operatorname{d}x (\!|\operatorname{d}y|\!)|\!)</math> | + | | <math>(\operatorname{d}x (\operatorname{d}y))\!</math> |
− | | <math>(\!|\operatorname{d}x\ \operatorname{d}y|\!)</math> | + | | <math>(\operatorname{d}x\ \operatorname{d}y)\!</math> |
| |- | | |- |
| | <math>f_{11}\!</math> | | | <math>f_{11}\!</math> |
− | | <math>(\!|x (\!|y|\!)|\!)</math> | + | | <math>(x (y))\!</math> |
− | | <math>(\!|(\!|\operatorname{d}x|\!) \operatorname{d}y|\!)</math> | + | | <math>((\operatorname{d}x) \operatorname{d}y)\!</math> |
− | | <math>(\!|(\!|\operatorname{d}x|\!)(\!|\operatorname{d}y|\!)|\!)</math> | + | | <math>((\operatorname{d}x)(\operatorname{d}y))\!</math> |
− | | <math>(\!|\operatorname{d}x\ \operatorname{d}y|\!)</math> | + | | <math>(\operatorname{d}x\ \operatorname{d}y)\!</math> |
− | | <math>(\!|\operatorname{d}x (\!|\operatorname{d}y|\!)|\!)</math> | + | | <math>(\operatorname{d}x (\operatorname{d}y))\!</math> |
| |- | | |- |
| | <math>f_{13}\!</math> | | | <math>f_{13}\!</math> |
− | | <math>(\!|(\!|x|\!) y|\!)</math> | + | | <math>((x) y)\!</math> |
− | | <math>(\!|\operatorname{d}x (\!|\operatorname{d}y|\!)|\!)</math> | + | | <math>(\operatorname{d}x (\operatorname{d}y))\!</math> |
− | | <math>(\!|\operatorname{d}x\ \operatorname{d}y|\!)</math> | + | | <math>(\operatorname{d}x\ \operatorname{d}y)\!</math> |
− | | <math>(\!|(\!|\operatorname{d}x|\!)(\!|\operatorname{d}y|\!)|\!)</math> | + | | <math>((\operatorname{d}x)(\operatorname{d}y))\!</math> |
− | | <math>(\!|(\!|\operatorname{d}x|\!) \operatorname{d}y|\!)</math> | + | | <math>((\operatorname{d}x) \operatorname{d}y)\!</math> |
| |- | | |- |
| | <math>f_{14}\!</math> | | | <math>f_{14}\!</math> |
− | | <math>(\!|(\!|x|\!)(\!|y|\!)|\!)</math> | + | | <math>((x)(y))\!</math> |
− | | <math>(\!|\operatorname{d}x\ \operatorname{d}y|\!)</math> | + | | <math>(\operatorname{d}x\ \operatorname{d}y)\!</math> |
− | | <math>(\!|\operatorname{d}x (\!|\operatorname{d}y|\!)|\!)</math> | + | | <math>(\operatorname{d}x (\operatorname{d}y))\!</math> |
− | | <math>(\!|(\!|\operatorname{d}x|\!) \operatorname{d}y|\!)</math> | + | | <math>((\operatorname{d}x) \operatorname{d}y)\!</math> |
− | | <math>(\!|(\!|\operatorname{d}x|\!)(\!|\operatorname{d}y|\!)|\!)</math> | + | | <math>((\operatorname{d}x)(\operatorname{d}y))\!</math> |
| |- | | |- |
| | <math>f_{15}\!</math> | | | <math>f_{15}\!</math> |
− | | <math>(\!|(\!|~|\!)|\!)</math> | + | | <math>((~))\!</math> |
− | | <math>(\!|(\!|~|\!)|\!)</math> | + | | <math>((~))\!</math> |
− | | <math>(\!|(\!|~|\!)|\!)</math> | + | | <math>((~))\!</math> |
− | | <math>(\!|(\!|~|\!)|\!)</math> | + | | <math>((~))\!</math> |
− | | <math>(\!|(\!|~|\!)|\!)</math> | + | | <math>((~))\!</math> |
| |}<br> | | |}<br> |
| | | |