MyWikiBiz, Author Your Legacy — Wednesday September 10, 2025
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3,050 bytes added
, 22:18, 29 May 2009
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| {| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%" | | {| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%" |
− | |+ <math>\text{Table 0.}~~\text{Propositional Forms on Two Variables}</math> | + | |+ <math>\text{Table A1.}~~\text{Propositional Forms on Two Variables}</math> |
| |- style="background:#f0f0ff" | | |- style="background:#f0f0ff" |
| | style="width:15%" | | | | style="width:15%" | |
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| | <math>\text{true}\!</math> | | | <math>\text{true}\!</math> |
| | <math>1\!</math> | | | <math>1\!</math> |
| + | |} |
| + | |
| + | <br> |
| + | |
| + | {| align="center" border="1" cellpadding="4" cellspacing="0" style="background:#f8f8ff; font-weight:bold; text-align:center; width:90%" |
| + | |+ '''Table A2. Propositional Forms on Two Variables''' |
| + | |- style="background:#f0f0ff" |
| + | ! width="15%" | L<sub>1</sub> |
| + | ! width="15%" | L<sub>2</sub> |
| + | ! width="15%" | L<sub>3</sub> |
| + | ! width="15%" | L<sub>4</sub> |
| + | ! width="25%" | L<sub>5</sub> |
| + | ! width="15%" | L<sub>6</sub> |
| + | |- style="background:#f0f0ff" |
| + | | |
| + | | align="right" | x : |
| + | | 1 1 0 0 |
| + | | |
| + | | |
| + | | |
| + | |- style="background:#f0f0ff" |
| + | | |
| + | | align="right" | y : |
| + | | 1 0 1 0 |
| + | | |
| + | | |
| + | | |
| + | |- |
| + | | f<sub>0</sub> |
| + | | f<sub>0000</sub> |
| + | | 0 0 0 0 |
| + | | ( ) |
| + | | false |
| + | | 0 |
| + | |- |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>f<sub>1</sub></p> |
| + | <p>f<sub>2</sub></p> |
| + | <p>f<sub>4</sub></p> |
| + | <p>f<sub>8</sub></p> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>f<sub>0001</sub></p> |
| + | <p>f<sub>0010</sub></p> |
| + | <p>f<sub>0100</sub></p> |
| + | <p>f<sub>1000</sub></p> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>0 0 0 1</p> |
| + | <p>0 0 1 0</p> |
| + | <p>0 1 0 0</p> |
| + | <p>1 0 0 0</p> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>(x)(y)</p> |
| + | <p>(x) y </p> |
| + | <p> x (y)</p> |
| + | <p> x y </p> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>neither x nor y</p> |
| + | <p>not x but y</p> |
| + | <p>x but not y</p> |
| + | <p>x and y</p> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>¬x ∧ ¬y</p> |
| + | <p>¬x ∧ y</p> |
| + | <p>x ∧ ¬y</p> |
| + | <p>x ∧ y</p> |
| + | |} |
| + | |- |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>f<sub>3</sub></p> |
| + | <p>f<sub>12</sub></p> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>f<sub>0011</sub></p> |
| + | <p>f<sub>1100</sub></p> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>0 0 1 1</p> |
| + | <p>1 1 0 0</p> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>(x)</p> |
| + | <p> x </p> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>not x</p> |
| + | <p>x</p> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>¬x</p> |
| + | <p>x</p> |
| + | |} |
| + | |- |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>f<sub>6</sub></p> |
| + | <p>f<sub>9</sub></p> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>f<sub>0110</sub></p> |
| + | <p>f<sub>1001</sub></p> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>0 1 1 0</p> |
| + | <p>1 0 0 1</p> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p> (x, y) </p> |
| + | <p>((x, y))</p> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>x not equal to y</p> |
| + | <p>x equal to y</p> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>x ≠ y</p> |
| + | <p>x = y</p> |
| + | |} |
| + | |- |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>f<sub>5</sub></p> |
| + | <p>f<sub>10</sub></p> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>f<sub>0101</sub></p> |
| + | <p>f<sub>1010</sub></p> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>0 1 0 1</p> |
| + | <p>1 0 1 0</p> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>(y)</p> |
| + | <p> y </p> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>not y</p> |
| + | <p>y</p> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>¬y</p> |
| + | <p>y</p> |
| + | |} |
| + | |- |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>f<sub>7</sub></p> |
| + | <p>f<sub>11</sub></p> |
| + | <p>f<sub>13</sub></p> |
| + | <p>f<sub>14</sub></p> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>f<sub>0111</sub></p> |
| + | <p>f<sub>1011</sub></p> |
| + | <p>f<sub>1101</sub></p> |
| + | <p>f<sub>1110</sub></p> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>0 1 1 1</p> |
| + | <p>1 0 1 1</p> |
| + | <p>1 1 0 1</p> |
| + | <p>1 1 1 0</p> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>(x y)</p> |
| + | <p>(x (y))</p> |
| + | <p>((x) y)</p> |
| + | <p>((x)(y))</p> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>not both x and y</p> |
| + | <p>not x without y</p> |
| + | <p>not y without x</p> |
| + | <p>x or y</p> |
| + | |} |
| + | | |
| + | {| align="center" |
| + | | |
| + | <p>¬x ∨ ¬y</p> |
| + | <p>x ⇒ y</p> |
| + | <p>x ⇐ y</p> |
| + | <p>x ∨ y</p> |
| + | |} |
| + | |- |
| + | | f<sub>15</sub> |
| + | | f<sub>1111</sub> |
| + | | 1 1 1 1 |
| + | | (( )) |
| + | | true |
| + | | 1 |
| |} | | |} |
| | | |