In mathematics and logic, a vacuous truth is a conditional or universal statement (a universal statement that can be converted to a conditional statement) that is true because the antecedent cannot be satisfied. ... One example of such a statement is "if London is in France, then the Eiffel Tower is in Bolivia".

Is vacuously true still true?

In logic, statements of type if P, then Q are said to be vacuously true when the proposition P is false. For example, the statement, if sun rises in the north then everyone gets 100 percent in final exam, is a true statement since the proposition "sun rises in the north" is false.

Can something be Vacuously false?

A "vacuously false" statement is vacuously false; although nobody ever gives this type of statement any thought. Example: Every element of the empty set is a purple flying elephant. We agree that this statement is (i) vacuous; it doesn't really say anything meaningful; and (ii) true by the laws of predicate logic.