Adverb
in a vacuous manner
Source: WordNetIn this case, the statement "all cell phones in the room are turned on" would also be vacuously true, as would the conjunction of the two: "all cell phones in the room are turned on and turned off". Source: Internet
Note that the empty set is a subset of every set (the statement that all elements of the empty set are also members of any set A is vacuously true ). Source: Internet
Outside of mathematics, statements which can be characterized informally as vacuously true can be misleading. Source: Internet
Proof: If there is no possible move, then the lemma is vacuously true (and the first player loses the normal play game by definition). Source: Internet