Example
The following statements are logically equivalent:
- If Lisa is in France, then she is in Europe. (In symbols, .)
- If Lisa is not in Europe, then she is not in France. (In symbols, .)
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.
(Note that in this example classical logic is assumed. Some non-classical logics do not deem (1) and (2) logically equivalent.)
Read more about this topic: Logical Equivalence
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