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\PMlinkescapeword{terms} \PMlinkescapeword{simple} \PMlinkescapeword{column} |
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| A contradictory statement is a statement (or form) which is false due to its logical form rather than because of the meaning of the terms employed. |
A contradictory statement is a statement (or form) which is false due to its logical form rather than because of the meaning of the terms employed. |
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| In propositional logic, a {\em contradictory statement}, a.k.a. {\em contradiction}, is a statement which is false regardless of the truth values of the substatements which form it.\, According to G. Peano, one may generally denote a contradiction with the symbol $\curlywedge$. |
In propositional logic, a {\em contradictory statement}, a.k.a. {\em contradiction}, is a statement which is false regardless of the truth values of the substatements which form it.\, According to G. Peano, one may generally denote a contradiction with the symbol $\curlywedge$. |
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| For a simple example, the statement\, $P\!\wedge\!\lnot P$\, is a contradiction for any statement $P$. |
For a simple example, the statement\, $P\!\wedge\!\lnot P$\, is a contradiction for any statement $P$. |
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| The negation $\lnot P$ of every contradiction $P$ is a tautology, and vice versa: |
The negation $\lnot P$ of every contradiction $P$ is a tautology, and vice versa: |
| $$\lnot\curlywedge = \curlyvee, \;\;\; \lnot\curlyvee = \curlywedge$$ |
$$\lnot\curlywedge = \curlyvee, \;\;\; \lnot\curlyvee = \curlywedge$$ |
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| To test a given statement or form to see if it is a contradiction, one may construct its truth table.\, If it turns out that every value of the last column is ``F'', then the statement is a contradiction. |
To test a given statement or form to see if it is a contradiction, one may construct its truth table.\, If it turns out that every value of the last column is ``F'', then the statement is a contradiction. |
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| Cf. the entry ``\PMlinkname{contradiction}{Contradiction}''. |
Cf. the entry ``\PMlinkname{contradiction}{Contradiction}''. |
