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Classification of Statements

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Tautology

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A tautology is a formula that is true in every possible interpretation. An example of a tautology is p¬pp \lor \neg p (for any proposition pp, either pp is true or pp is false).

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Contradiction

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A contradiction is a formula that is false under every possible interpretation. An example of a contradiction is p¬pp \land \neg p (a proposition pp cannot be both true and false at the same time).

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Contingency

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A contingency is a formula that can be either true or false depending on the interpretation. An example is the proposition pqp \lor q (which is true if either pp or qq are true, false otherwise).

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Logical Equivalence

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Two statements are logically equivalent if they have the same truth value in every possible interpretation. An example is pqp \rightarrow q is logically equivalent to ¬pq\neg p \lor q.

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