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''.