MyWikiBiz, Author Your Legacy — Friday November 22, 2024
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, 18:20, 17 January 2008
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| : ''e''<sub>1</sub> ''e''<sub>2</sub> ''e''<sub>3</sub> means "''e''<sub>1</sub> and ''e''<sub>2</sub> and ''e''<sub>3</sub>". | | : ''e''<sub>1</sub> ''e''<sub>2</sub> ''e''<sub>3</sub> means "''e''<sub>1</sub> and ''e''<sub>2</sub> and ''e''<sub>3</sub>". |
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− | The bound connectives are written as lists of ''k'' expressions (''e''<sub>1</sub>, …, ''e''<sub>''k''</sub>), where the parentheses and commas are considered to be parts of the connective notation. In text presentations the parentheses will be superscripted, as <sup>(</sup>''e''<sub>1</sub>, …, ''e''<sub>''k''</sub><sup>)</sup>, to avoid confusion with other uses. The bound connective is interpreted to mean that just one of the ''k'' listed expressions is false. That is, <sup>(</sup>''e''<sub>1</sub>, …, ''e''<sub>''k''</sub><sup>)</sup> is true if and only if exactly one of the expressions ''e''<sub>1</sub>, …, ''e''<sub>''k''</sub> is false. In particular, for ''k'' = 1 and 2: | + | The bound connectives are written as lists of ''k'' expressions (''e''<sub>1</sub>, …, ''e''<sub>''k''</sub>), where the parentheses and commas are considered to be parts of the connective notation. In text presentations the parentheses will be superscripted, as <sup>(</sup>''e''<sub>1</sub>, …, ''e''<sub>''k''</sub><sup>)</sup>, to avoid confusion with other uses. The bound connective is interpreted to mean that just one of the ''k'' listed expressions is false. That is, <sup>(</sup>''e''<sub>1</sub>, …, ''e''<sub>''k''</sub><sup>)</sup> is true if and only if exactly one of the expressions ''e''<sub>1</sub>, …, ''e''<sub>''k''</sub> is false. In particular, for ''k'' = 1 and 2, we have: |
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− | <pre> | + | :{| cellpadding="4" |
− | (e1) means "not e1".
| + | | (''e''<sub>1</sub>) |
− | | + | | means |
− | (e1,e2) means "e1 xor e2", "e1 + e2",
| + | | not ''e''<sub>1</sub>. |
− | | + | | |
− | or "e1 neq e2", "e1 =/= e2".
| + | |- |
− | </pre> | + | | (''e''<sub>1</sub>, ''e''<sub>2</sub>) |
| + | | means |
| + | | ''e''<sub>1</sub> xor ''e''<sub>2</sub>, |
| + | | ''e''<sub>1</sub> + ''e''<sub>2</sub>, |
| + | |- |
| + | | |
| + | | or |
| + | | ''e''<sub>1</sub> neq ''e''<sub>2</sub>, |
| + | | ''e''<sub>1</sub> ≠ ''e''<sub>2</sub>. |
| + | |} |
| | | |
| A remaining sample of typical expressions will finish illustrating the use of this calculus. | | A remaining sample of typical expressions will finish illustrating the use of this calculus. |