Line 1,477: |
Line 1,477: |
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| |- | | |- |
− | | <math>f_{0}\!</math> | + | | |
− | | <math>f_{0000}\!</math> | + | {| align="center" |
− | | <math>0~0~0~0\!</math> | + | | |
− | | <math>(~)\!</math> | + | <math>\begin{matrix} |
− | | <math>\text{false}\!</math> | + | f_0 |
− | | <math>0\!</math> | + | \\[4pt] |
| + | f_1 |
| + | \\[4pt] |
| + | f_2 |
| + | \\[4pt] |
| + | f_3 |
| + | \\[4pt] |
| + | f_4 |
| + | \\[4pt] |
| + | f_5 |
| + | \\[4pt] |
| + | f_6 |
| + | \\[4pt] |
| + | f_7 |
| + | \end{matrix}</math> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <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> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <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> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <math>\begin{matrix} |
| + | (~) |
| + | \\[4pt] |
| + | (x)(y) |
| + | \\[4pt] |
| + | (x)~y~ |
| + | \\[4pt] |
| + | (x)~~~ |
| + | \\[4pt] |
| + | ~x~(y) |
| + | \\[4pt] |
| + | ~~~(y) |
| + | \\[4pt] |
| + | (x,~y) |
| + | \\[4pt] |
| + | (x~~y) |
| + | \end{matrix}</math> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <math>\begin{matrix} |
| + | \text{false} |
| + | \\[4pt] |
| + | \text{neither}~ x ~\text{nor}~ y |
| + | \\[4pt] |
| + | y ~\text{without}~ x |
| + | \\[4pt] |
| + | \text{not}~ x |
| + | \\[4pt] |
| + | x ~\text{without}~ y |
| + | \\[4pt] |
| + | \text{not}~ y |
| + | \\[4pt] |
| + | x ~\text{not equal to}~ y |
| + | \\[4pt] |
| + | \text{not both}~ x ~\text{and}~ y |
| + | \end{matrix}</math> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <math>\begin{matrix} |
| + | 0 |
| + | \\[4pt] |
| + | \lnot x \land \lnot y |
| + | \\[4pt] |
| + | \lnot x \land y |
| + | \\[4pt] |
| + | \lnot x |
| + | \\[4pt] |
| + | x \land \lnot y |
| + | \\[4pt] |
| + | \lnot y |
| + | \\[4pt] |
| + | x \ne y |
| + | \\[4pt] |
| + | \lnot x \lor \lnot y |
| + | \end{matrix}</math> |
| + | |} |
| |- | | |- |
− | | <math>f_{1}\!</math> | + | | |
− | | <math>f_{0001}\!</math> | + | {| align="center" |
− | | <math>0~0~0~1\!</math>
| + | | |
− | | <math>(x)(y)\!</math>
| + | <math>\begin{matrix} |
− | | <math>\text{neither}~ x ~\text{nor}~ y\!</math>
| + | f_8 |
− | | <math>\lnot x \land \lnot y\!</math>
| + | \\[4pt] |
− | |-
| + | f_9 |
− | | <math>f_{2}\!</math>
| + | \\[4pt] |
− | | <math>f_{0010}\!</math>
| + | f_{10} |
− | | <math>0~0~1~0\!</math>
| + | \\[4pt] |
− | | <math>(x)~y\!</math>
| + | f_{11} |
− | | <math>y ~\text{without}~ x\!</math>
| + | \\[4pt] |
− | | <math>\lnot x \land y\!</math>
| + | f_{12} |
− | |-
| + | \\[4pt] |
− | | <math>f_{3}\!</math>
| + | f_{13} |
− | | <math>f_{0011}\!</math> | + | \\[4pt] |
− | | <math>0~0~1~1\!</math> | + | f_{14} |
− | | <math>(x)\!</math> | + | \\[4pt] |
− | | <math>\text{not}~ x\!</math> | + | f_{15} |
− | | <math>\lnot x\!</math>
| + | \end{matrix}</math> |
− | |-
| + | |} |
− | | <math>f_{4}\!</math>
| + | | |
− | | <math>f_{0100}\!</math>
| + | {| align="center" |
− | | <math>0~1~0~0\!</math>
| + | | |
− | | <math>x~(y)\!</math>
| + | <math>\begin{matrix} |
− | | <math>x ~\text{without}~ y\!</math>
| + | f_{1000} |
− | | <math>x \land \lnot y\!</math>
| + | \\[4pt] |
− | |-
| + | f_{1001} |
− | | <math>f_{5}\!</math>
| + | \\[4pt] |
− | | <math>f_{0101}\!</math>
| + | f_{1010} |
− | | <math>0~1~0~1\!</math>
| + | \\[4pt] |
− | | <math>(y)\!</math>
| + | f_{1011} |
− | | <math>\text{not}~ y\!</math>
| + | \\[4pt] |
− | | <math>\lnot y\!</math>
| + | f_{1100} |
− | |-
| + | \\[4pt] |
− | | <math>f_{6}\!</math>
| + | f_{1101} |
− | | <math>f_{0110}\!</math> | + | \\[4pt] |
− | | <math>0~1~1~0\!</math> | + | f_{1110} |
− | | <math>(x,~y)\!</math> | + | \\[4pt] |
− | | <math>x ~\text{not equal to}~ y\!</math> | + | f_{1111} |
− | | <math>x \ne y\!</math>
| + | \end{matrix}</math> |
− | |-
| + | |} |
− | | <math>f_{7}\!</math>
| + | | |
− | | <math>f_{0111}\!</math>
| + | {| align="center" |
− | | <math>0~1~1~1\!</math>
| + | | |
− | | <math>(x~y)\!</math>
| + | <math>\begin{matrix} |
− | | <math>\text{not both}~ x ~\text{and}~ y\!</math>
| + | 1~0~0~0 |
− | | <math>\lnot x \lor \lnot y\!</math>
| + | \\[4pt] |
− | |-
| + | 1~0~0~1 |
− | | <math>f_{8}\!</math>
| + | \\[4pt] |
− | | <math>f_{1000}\!</math>
| + | 1~0~1~0 |
− | | <math>1~0~0~0\!</math>
| + | \\[4pt] |
− | | <math>x~y\!</math>
| + | 1~0~1~1 |
− | | <math>x ~\text{and}~ y\!</math>
| + | \\[4pt] |
− | | <math>x \land y\!</math> | + | 1~1~0~0 |
− | |- | + | \\[4pt] |
− | | <math>f_{9}\!</math> | + | 1~1~0~1 |
− | | <math>f_{1001}\!</math> | + | \\[4pt] |
− | | <math>1~0~0~1\!</math>
| + | 1~1~1~0 |
− | | <math>((x,~y))\!</math>
| + | \\[4pt] |
− | | <math>x ~\text{equal to}~ y\!</math>
| + | 1~1~1~1 |
− | | <math>x = y\!</math>
| + | \end{matrix}</math> |
− | |-
| + | |} |
− | | <math>f_{10}\!</math>
| + | | |
− | | <math>f_{1010}\!</math>
| + | {| align="center" |
− | | <math>1~0~1~0\!</math>
| + | | |
− | | <math>y\!</math>
| + | <math>\begin{matrix} |
− | | <math>y\!</math>
| + | ~~x~~y~~ |
− | | <math>y\!</math>
| + | \\[4pt] |
− | |-
| + | ((x,~y)) |
− | | <math>f_{11}\!</math>
| + | \\[4pt] |
− | | <math>f_{1011}\!</math> | + | ~~~~~y~~ |
− | | <math>1~0~1~1\!</math> | + | \\[4pt] |
− | | <math>(x~(y))\!</math> | + | ~(x~(y)) |
− | | <math>\text{not}~ x ~\text{without}~ y\!</math> | + | \\[4pt] |
− | | <math>x \Rightarrow y\!</math>
| + | ~~x~~~~~ |
− | |-
| + | \\[4pt] |
− | | <math>f_{12}\!</math>
| + | ((x)~y)~ |
− | | <math>f_{1100}\!</math>
| + | \\[4pt] |
− | | <math>1~1~0~0\!</math>
| + | ((x)(y)) |
− | | <math>x\!</math>
| + | \\[4pt] |
− | | <math>x\!</math>
| + | ((~)) |
− | | <math>x\!</math>
| + | \end{matrix}</math> |
− | |-
| + | |} |
− | | <math>f_{13}\!</math>
| + | | |
− | | <math>f_{1101}\!</math>
| + | {| align="center" |
− | | <math>1~1~0~1\!</math>
| + | | |
− | | <math>((x)~y)\!</math>
| + | <math>\begin{matrix} |
− | | <math>\text{not}~ y ~\text{without}~ x\!</math>
| + | x ~\text{and}~ y |
− | | <math>x \Leftarrow y\!</math>
| + | \\[4pt] |
− | |- | + | x ~\text{equal to}~ y |
− | | <math>f_{14}\!</math> | + | \\[4pt] |
− | | <math>f_{1110}\!</math> | + | y |
− | | <math>1~1~1~0\!</math>
| + | \\[4pt] |
− | | <math>((x)(y))\!</math>
| + | \text{not}~ x ~\text{without}~ y |
− | | <math>x ~\text{or}~ y\!</math>
| + | \\[4pt] |
− | | <math>x \lor y\!</math>
| + | x |
− | |-
| + | \\[4pt] |
− | | <math>f_{15}\!</math>
| + | \text{not}~ y ~\text{without}~ x |
− | | <math>f_{1111}\!</math>
| + | \\[4pt] |
− | | <math>1~1~1~1\!</math>
| + | x ~\text{or}~ y |
− | | <math>((~))\!</math>
| + | \\[4pt] |
− | | <math>\text{true}\!</math>
| + | \text{true} |
− | | <math>1\!</math> | + | \end{matrix}</math> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <math>\begin{matrix} |
| + | x \land y |
| + | \\[4pt] |
| + | x = y |
| + | \\[4pt] |
| + | y |
| + | \\[4pt] |
| + | x \Rightarrow y |
| + | \\[4pt] |
| + | x |
| + | \\[4pt] |
| + | x \Leftarrow y |
| + | \\[4pt] |
| + | x \lor y |
| + | \\[4pt] |
| + | 1 |
| + | \end{matrix}</math> |
| + | |} |
| |} | | |} |
| | | |