In logic, statements p and q are logically equivalent if they have the same logical content.

Syntactically, p and q are equivalent if each can be proved from the other. Semantically, p and q are equivalent if they have the same truth value in every model.

The logical equivalence of p and q is sometimes expressed as Failed to parse (Missing texvc executable; please see math/README to configure.): p \equiv q , Epq, or Failed to parse (Missing texvc executable; please see math/README to configure.): p \Leftrightarrow q . However, these symbols are also used for material equivalence; the proper interpretation depends on the context. Logical equivalence is different from material equivalence, although the two concepts are closely related.

The following statements are logically equivalent:

.)

.)

Syntactically, (1) and (2) are derivable from each other via the rules of contraposition and double negation. Semantically, (1) and (2) are true in exactly the same models (interpretations, valuations); namely, those in which either Lisa is in France is false or Lisa is in Europe is true.