Editing Logical equivalence (section)

==Examples==

=== In logic ===
The following statements are logically equivalent:

#If Lisa is in [[Denmark]], then she is in [[Europe]] (a statement of the form <math>d \rightarrow e</math>).
#If Lisa is not in Europe, then she is not in Denmark (a statement of the form <math>\neg e \rightarrow \neg d</math>).

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 Denmark'' is false or ''Lisa is in Europe'' is true.

(Note that in this example, [[classical logic]] is assumed. Some [[non-classical logic]]s do not deem (1) and (2) to be logically equivalent.)