Several statements above explicitly include "X", the set of elements that the quantifier applies to. This set of elements is also known as the range of quantification, or the universe of discourse. Some of the statements above do not include such a set. In this case, the set will have to be specified before the statement. For example, ""x" is an apple" must be stated before formula_12. In this case, we are making a statement that at least one apple fits the predicate "P".