Contradictory Statement
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A Contradictory Statement is a Formal Statement where ...
- AKA: Contradiction.
- See: Truth Table, Statement.
References
- http://planetmath.org/encyclopedia/ContradictoryStatement.html
- 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.