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# contradictory statement

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.

In propositional logic, a contradictory statement, a.k.a. 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 $\curlywedge$.

For a simple example, the statement $P\!\wedge\!\lnot P$ is a contradiction for any statement $P$.

The negation $\lnot Q$ of every contradiction $Q$ is a tautology, and vice versa:

$\lnot\curlywedge=\curlyvee,\;\;\;\lnot\curlyvee=\curlywedge$ |

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.

Cf. the entry “contradiction”.

## Mathematics Subject Classification

03B05*no label found*

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