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. For example, the statement "she does not own a cell phone" will imply that the statement "all of her cell phones are turned off" will be assigned a truth value. Additionally, the statement "all of her cell phones are turned on" would also be vacuously true, as would the conjunction of Mo...