A claim that is technically true but meaningless, in the form of claiming that no A in B has C, when there are no A in B. For example, claiming that no mobile phones in the room are on when there are no mobile phones in the room at all.
A statement that asserts that all members of the empty set have a certain property. More formally, a relatively well-defined usage refers to a conditional statement with a false antecedent. Such statements are considered vacuous because the fact that the antecedent is false prevents using the statement to infer anything about the truth value of the consequent.
They are true because a material conditional is defined to be true when the antecedent is false (regardless of whether the conclusion is true).
Statements which can be characterized informally as vacuously true can be misleading. Such statements make reasonable assertions about qualified objects which do not actually exist.
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Idioms, Fallacies, and Paradoxes
RandomAll definitions are 100% written by Wikipedia, not my own words.
