MyWikiBiz, Author Your Legacy — Tuesday September 09, 2025
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1,133 bytes added
, 01:36, 30 May 2009
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− | | f<sub>0</sub> | + | | <math>f_0\!</math> |
− | | f<sub>0000</sub> | + | | <math>f_{0000}\!</math> |
− | | 0 0 0 0 | + | | <math>0~0~0~0</math> |
− | | ( ) | + | | <math>(~)</math> |
− | | false | + | | <math>\text{false}\!</math> |
− | | 0 | + | | <math>0\!</math> |
| |- | | |- |
| | | | | |
| {| align="center" | | {| align="center" |
| | | | | |
− | <p>f<sub>1</sub></p> | + | <math>\begin{matrix} |
− | <p>f<sub>2</sub></p>
| + | f_1 |
− | <p>f<sub>4</sub></p>
| + | \\[4pt] |
− | <p>f<sub>8</sub></p>
| + | f_2 |
| + | \\[4pt] |
| + | f_4 |
| + | \\[4pt] |
| + | f_8 |
| + | \end{matrix}</math> |
| |} | | |} |
| | | | | |
| {| align="center" | | {| align="center" |
| | | | | |
− | <p>f<sub>0001</sub></p> | + | <math>\begin{matrix} |
− | <p>f<sub>0010</sub></p>
| + | f_{0001} |
− | <p>f<sub>0100</sub></p>
| + | \\[4pt] |
− | <p>f<sub>1000</sub></p>
| + | f_{0010} |
| + | \\[4pt] |
| + | f_{0100} |
| + | \\[4pt] |
| + | f_{1000} |
| + | \end{matrix}</math> |
| |} | | |} |
| | | | | |
| {| align="center" | | {| align="center" |
| | | | | |
− | <p>0 0 0 1</p> | + | <math>\begin{matrix} |
− | <p>0 0 1 0</p>
| + | 0~0~0~1 |
− | <p>0 1 0 0</p>
| + | \\[4pt] |
− | <p>1 0 0 0</p>
| + | 0~0~1~0 |
| + | \\[4pt] |
| + | 0~1~0~0 |
| + | \\[4pt] |
| + | 1~0~0~0 |
| + | \end{matrix}</math> |
| |} | | |} |
| | | | | |
| {| align="center" | | {| align="center" |
| | | | | |
− | <p>(x)(y)</p> | + | <math>\begin{matrix} |
− | <p>(x) y </p>
| + | (x)(y) |
− | <p> x (y)</p>
| + | \\[4pt] |
− | <p> x y </p>
| + | (x)~y~ |
| + | \\[4pt] |
| + | ~x~(y) |
| + | \\[4pt] |
| + | ~x~~y~ |
| + | \end{matrix}</math> |
| |} | | |} |
| | | | | |
| {| align="center" | | {| align="center" |
| | | | | |
− | <p>neither x nor y</p> | + | <math>\begin{matrix} |
− | <p>not x but y</p>
| + | \text{neither}~ x ~\text{nor}~ y |
− | <p>x but not y</p>
| + | \\[4pt] |
− | <p>x and y</p>
| + | y ~\text{without}~ x |
| + | \\[4pt] |
| + | x ~\text{without}~ y |
| + | \\[4pt] |
| + | x ~\text{and}~ y |
| + | \end{matrix}</math> |
| |} | | |} |
| | | | | |
| {| align="center" | | {| align="center" |
| | | | | |
− | <p>¬x ∧ ¬y</p> | + | <math>\begin{matrix} |
− | <p>¬x ∧ y</p>
| + | \lnot x \land \lnot y |
− | <p>x ∧ ¬y</p>
| + | \\[4pt] |
− | <p>x ∧ y</p>
| + | \lnot x \land y |
| + | \\[4pt] |
| + | x \land \lnot y |
| + | \\[4pt] |
| + | x \land y |
| + | \end{matrix}</math> |
| |} | | |} |
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| {| align="center" | | {| align="center" |
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− | <p>f<sub>3</sub></p> | + | <math>\begin{matrix} |
− | <p>f<sub>12</sub></p>
| + | f_3 |
| + | \\[4pt] |
| + | f_{12} |
| + | \end{matrix}</math> |
| |} | | |} |
| | | | | |
| {| align="center" | | {| align="center" |
| | | | | |
− | <p>f<sub>0011</sub></p> | + | <math>\begin{matrix} |
− | <p>f<sub>1100</sub></p>
| + | f_{0011} |
| + | \\[4pt] |
| + | f_{1100} |
| + | \end{matrix}</math> |
| |} | | |} |
| | | | | |
| {| align="center" | | {| align="center" |
| | | | | |
− | <p>0 0 1 1</p> | + | <math>\begin{matrix} |
− | <p>1 1 0 0</p>
| + | 0~0~1~1 |
| + | \\[4pt] |
| + | 1~1~0~0 |
| + | \end{matrix}</math> |
| |} | | |} |
| | | | | |
| {| align="center" | | {| align="center" |
| | | | | |
− | <p>(x)</p> | + | <math>\begin{matrix} |
− | <p> x </p>
| + | (x) |
| + | \\[4pt] |
| + | ~x~ |
| + | \end{matrix}</math> |
| |} | | |} |
| | | | | |
| {| align="center" | | {| align="center" |
| | | | | |
− | <p>not x</p> | + | <math>\begin{matrix} |
− | <p>x</p>
| + | \text{not}~ x |
| + | \\[4pt] |
| + | x |
| + | \end{matrix}</math> |
| |} | | |} |
| | | | | |
| {| align="center" | | {| align="center" |
| | | | | |
− | <p>¬x</p> | + | <math>\begin{matrix} |
− | <p>x</p>
| + | \lnot x |
| + | \\[4pt] |
| + | x |
| + | \end{matrix}</math> |
| |} | | |} |
| |- | | |- |
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| {| align="center" | | {| align="center" |
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− | <p>f<sub>6</sub></p> | + | <math>\begin{matrix} |
− | <p>f<sub>9</sub></p>
| + | f_6 |
| + | \\[4pt] |
| + | f_9 |
| + | \end{matrix}</math> |
| |} | | |} |
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| {| align="center" | | {| align="center" |
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− | <p>f<sub>0110</sub></p> | + | <math>\begin{matrix} |
− | <p>f<sub>1001</sub></p>
| + | f_{0110} |
| + | \\[4pt] |
| + | f_{1001} |
| + | \end{matrix}</math> |
| |} | | |} |
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| {| align="center" | | {| align="center" |
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− | <p>0 1 1 0</p> | + | <math>\begin{matrix} |
− | <p>1 0 0 1</p>
| + | 0~1~1~0 |
| + | \\[4pt] |
| + | 1~0~0~1 |
| + | \end{matrix}</math> |
| |} | | |} |
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| {| align="center" | | {| align="center" |
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− | <p> (x, y) </p> | + | <math>\begin{matrix} |
− | <p>((x, y))</p>
| + | ~(x,~y)~ |
| + | \\[4pt] |
| + | ((x,~y)) |
| + | \end{matrix}</math> |
| |} | | |} |
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| {| align="center" | | {| align="center" |
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− | <p>x not equal to y</p> | + | <math>\begin{matrix} |
− | <p>x equal to y</p>
| + | x ~\text{not equal to}~ y |
| + | \\[4pt] |
| + | x ~\text{equal to}~ y |
| + | \end{matrix}</math> |
| |} | | |} |
| | | | | |
| {| align="center" | | {| align="center" |
| | | | | |
− | <p>x ≠ y</p> | + | <math>\begin{matrix} |
− | <p>x = y</p>
| + | x \ne y |
| + | \\[4pt] |
| + | x = y |
| + | \end{matrix}</math> |
| |} | | |} |
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| {| align="center" | | {| align="center" |
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− | <p>f<sub>5</sub></p> | + | <math>\begin{matrix} |
− | <p>f<sub>10</sub></p>
| + | f_5 |
| + | \\[4pt] |
| + | f_{10} |
| + | \end{matrix}</math> |
| |} | | |} |
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| {| align="center" | | {| align="center" |
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− | <p>f<sub>0101</sub></p> | + | <math>\begin{matrix} |
− | <p>f<sub>1010</sub></p>
| + | f_{0101} |
| + | \\[4pt] |
| + | f_{1010} |
| + | \end{matrix}</math> |
| |} | | |} |
| | | | | |
| {| align="center" | | {| align="center" |
| | | | | |
− | <p>0 1 0 1</p> | + | <math>\begin{matrix} |
− | <p>1 0 1 0</p>
| + | 0~1~0~1 |
| + | \\[4pt] |
| + | 1~0~1~0 |
| + | \end{matrix}</math> |
| |} | | |} |
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| {| align="center" | | {| align="center" |
| | | | | |
− | <p>(y)</p> | + | <math>\begin{matrix} |
− | <p> y </p>
| + | (y) |
| + | \\[4pt] |
| + | ~y~ |
| + | \end{matrix}</math> |
| |} | | |} |
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| {| align="center" | | {| align="center" |
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− | <p>not y</p> | + | <math>\begin{matrix} |
− | <p>y</p>
| + | \text{not}~ y |
| + | \\[4pt] |
| + | y |
| + | \end{matrix}</math> |
| |} | | |} |
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| {| align="center" | | {| align="center" |
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− | <p>¬y</p> | + | <math>\begin{matrix} |
− | <p>y</p>
| + | \lnot y |
| + | \\[4pt] |
| + | y |
| + | \end{matrix}</math> |
| |} | | |} |
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| {| align="center" | | {| align="center" |
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− | <p>f<sub>7</sub></p> | + | <math>\begin{matrix} |
− | <p>f<sub>11</sub></p>
| + | f_7 |
− | <p>f<sub>13</sub></p>
| + | \\[4pt] |
− | <p>f<sub>14</sub></p>
| + | f_{11} |
| + | \\[4pt] |
| + | f_{13} |
| + | \\[4pt] |
| + | f_{14} |
| + | \end{matrix}</math> |
| |} | | |} |
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| {| align="center" | | {| align="center" |
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− | <p>f<sub>0111</sub></p> | + | <math>\begin{matrix} |
− | <p>f<sub>1011</sub></p>
| + | f_{0111} |
− | <p>f<sub>1101</sub></p>
| + | \\[4pt] |
− | <p>f<sub>1110</sub></p>
| + | f_{1011} |
| + | \\[4pt] |
| + | f_{1101} |
| + | \\[4pt] |
| + | f_{1110} |
| + | \end{matrix}</math> |
| |} | | |} |
| | | | | |
| {| align="center" | | {| align="center" |
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− | <p>0 1 1 1</p> | + | <math>\begin{matrix} |
− | <p>1 0 1 1</p>
| + | 0~1~1~1 |
− | <p>1 1 0 1</p>
| + | \\[4pt] |
− | <p>1 1 1 0</p>
| + | 1~0~1~1 |
| + | \\[4pt] |
| + | 1~1~0~1 |
| + | \\[4pt] |
| + | 1~1~1~0 |
| + | \end{matrix}</math> |
| |} | | |} |
| | | | | |
| {| align="center" | | {| align="center" |
| | | | | |
− | <p>(x y)</p> | + | <math>\begin{matrix} |
− | <p>(x (y))</p>
| + | ~(x~~y)~ |
− | <p>((x) y)</p>
| + | \\[4pt] |
− | <p>((x)(y))</p>
| + | ~(x~(y)) |
| + | \\[4pt] |
| + | ((x)~y)~ |
| + | \\[4pt] |
| + | ((x)(y)) |
| + | \end{matrix}</math> |
| |} | | |} |
| | | | | |
| {| align="center" | | {| align="center" |
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− | <p>not both x and y</p> | + | <math>\begin{matrix} |
− | <p>not x without y</p>
| + | \text{not both}~ x ~\text{and}~ y |
− | <p>not y without x</p>
| + | \\[4pt] |
− | <p>x or y</p>
| + | \text{not}~ x ~\text{without}~ y |
| + | \\[4pt] |
| + | \text{not}~ y ~\text{without}~ x |
| + | \\[4pt] |
| + | x ~\text{or}~ y |
| + | \end{matrix}</math> |
| |} | | |} |
| | | | | |
| {| align="center" | | {| align="center" |
| | | | | |
− | <p>¬x ∨ ¬y</p> | + | <math>\begin{matrix} |
− | <p>x ⇒ y</p>
| + | \lnot x \lor \lnot y |
− | <p>x ⇐ y</p>
| + | \\[4pt] |
− | <p>x ∨ y</p>
| + | x \Rightarrow y |
| + | \\[4pt] |
| + | x \Leftarrow y |
| + | \\[4pt] |
| + | x \lor y |
| + | \end{matrix}</math> |
| |} | | |} |
| |- | | |- |
− | | f<sub>15</sub> | + | | <math>f_{15}\!</math> |
− | | f<sub>1111</sub> | + | | <math>f_{1111}\!</math> |
− | | 1 1 1 1 | + | | <math>1~1~1~1</math> |
− | | (( )) | + | | <math>((~))</math> |
− | | true | + | | <math>\text{true}\!</math> |
− | | 1 | + | | <math>1\!</math> |
| |} | | |} |
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