the domain of discourse, which specifies which values n can take. In particular, note that if the domain of discourse is restricted to consist only of those objects that satisfy a certain predicate, then for universal quantification this requires a logical conditional. For example, For all composite numbers n, one has 2·n > 2 + n is logically equivalent to For all natural numbers n, if n is composite, then 2·n > 2 + n. Here the "if ... then" construction indicates the logical conditional. Notation In symbolic logic, the universal quantifier symbol (a turned "A" in a sans-serif font, Unicode U+2200) is used to indicate universal quantification. It was first used in this way by Gerhard Gentzen in 1935, by analogy with Giuseppe Peano's (turned E) notation for existential quantification and the later use of Peano's notation by Bertrand Russell. For example, if P(n) is the predicate "2·n > 2 + n" and N is the set of natural numbers, then is the (false) statement "for all natural numbers n, one has 2·n > 2 + n". Similarly, if Q(n) is the predicate "n is composite", then is the (true) statement "for all natural numbers n, if n is composite, then ". Several variations in the notation for quantification (which apply to all forms) can be found in the Quantifier article. Properties Negation The negation of a universally quantified function is obtained by changing the universal quantifier into an existential quantifier and negating the quantified formula. That is, where denotes negation. For example, if is the propositional function " is married", then, for the set of all living human beings, the universal quantification Given any living person , that person is married is written This statement is false. Truthfully, it is stated that It is not the case that, given any living person , that person is married or, symbolically: . If the function is not true for every element of , then there must be at least one element for which the statement is false. That is, the negation of is logically equivalent to "There exists a living person who is not married", or: It is erroneous to confuse "all persons are not married" (i.e. "there exists no person who is married") with "not all persons are married" (i.e. "there exists a person who is not married"): Other connectives The universal (and existential) quantifier moves unchanged across the