[1][3][2][4] One example of such a statement is "if Tokyo is in Spain, then the Eiffel Tower is in Bolivia".
In essence, a conditional statement, that is based on the material conditional, is true when the antecedent ("Tokyo is in Spain" in the example) is false regardless of whether the conclusion or consequent ("the Eiffel Tower is in Bolivia" in the example) is true or false because the material conditional is defined in that way.
Examples common to everyday speech include conditional phrases used as idioms of improbability like "when hell freezes over ..." and "when pigs can fly ...", indicating that not before the given (impossible) condition is met will the speaker accept some respective (typically false or absurd) proposition.
[5] This notion has relevance in pure mathematics, as well as in any other field that uses classical logic.
Outside of mathematics, statements in the form of a vacuous truth, while logically valid, can nevertheless be misleading.
Such statements make reasonable assertions about qualified objects which do not actually exist.
[1][3][2] Vacuously true statements that can be reduced (with suitable transformations) to this basic form (material conditional) include the following universally quantified statements: Vacuous truths most commonly appear in classical logic with two truth values.