👉 Nonvacuousness in mathematics refers to a property of mathematical objects that means they can be both true and false simultaneously, without any contradictory statements or conditions. In other words, it is a property that allows for multiple interpretations of a statement. For example, consider the set of all real numbers. This set does not contain any nonvacuous elements because every element in this set is either a real number itself (true) or an empty set (false). Thus, there are no contradictions within this