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There are various normal forms which have been identified for relational databases. Higher levels of normalization lead to designs that reduce data redundancy and avoid the update anomalies mentioned above. Any higher normal form also conforms to all lower normal forms. Thus, a relation in third normal form (3NF) is also in second normal form (2NF), and first normal form (1NF). Discussions of normal forms rely upon the concept of functional dependency. When the value of one attribute, or set of attributes, determines the value of another attribute, a functional dependency exists, and the first attribute, or set of attributes, is called the determinant. Suppose that we created a relation with the attributes shown in Figure 8.3.
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Figure 8-3 Student relation.
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The key of the Student relation is the composite of Sname and Dorm (assuming that no students with the same name will live in the same dorm). This horizontal box representation is a common way to represent a relation vertical lines separate the attribute names, and the attributes that comprise the key are underlined. The key attributes do not need to be adjacent to one another, and they do not need to be on the left side, but often people choose to show them this way. The key of any relation is always a determinant; by definition, the key identifies the entire tuple. Given values for Sname and Dorm in the Student relation, the values for all the other attributes are determined. Not all determinants are keys, however. In the Student relation, there is a functional dependency between MajorAdvisorName and AdvisorDept. Given a value for the advisor name, the department value is determined. First normal form is simply the definition of a relation. Each attribute must be an atomic, single-valued attribute. For example, if an attribute in the Student relation is TelephoneNumber, any one tuple in the relation can have only one value for TelephoneNumber. If one wants to store multiple telephone numbers for a student, then one must create a separate relation for that purpose. Then each tuple in the new PhoneNumber relation can have a single telephone number, and multiple tuples in the PhoneNumber relation can be associated via a 1:N relationship with a particular student. Second normal form requires that every nonkey attribute be functionally dependent on the entire key. Said another way, each nonkey attribute value must provide a fact about the entity as a whole, not a fact about a part of the key. If the key of a relation is a single attribute value, for example a surrogate key, any relation is automatically in 2NF. All the nonkey attributes are dependent on (i.e., determined by) the key. Without thinking too much about it, anyone might think that the Student relation is a reasonable design for a database that will track students. On closer reflection, however, note that the relation includes information about resident advisors (RAs), and faculty advisors, as well as about students. Is every non-key attribute in the Student relation dependent upon (determined by) values of the entire key In this case, the answer is No. Assuming that there is one RA per Dorm, then the value of RA depends upon Dorm, but not upon Sname. To bring the design into 2NF, make a new relation called Dorm, and remove the RA attribute from the Student relation (Fig. 8.4).
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Figure 8-4 2NF.
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This is progress, but it s still true that the Student relation tracks information about something other than students. In particular, the relation is tracking information about advisors; it s tracking not just who the advisor for each student is, but also what department the advisor belongs to. If a relation is to focus on a single theme, this doesn t seem right. Third normal form requires that a relation has no transitive dependencies. Said another way, each non-key attribute must provide a fact about the entity as a whole, not about another nonkey attribute. That is what is still wrong with the Student relation. MajorAdvisorName and AdvisorDept are both dependent upon the key of the Student relation, but AdvisorDept is also transitively dependent upon MajorAdvisorName. Once we know who the student is, we can determine the student s advisor, and once we know the advisor, we can determine the advisor s department. This is a transitive dependency: A determines B, and B determines C. To make the design conform to 3NF, one must remove the transitive dependency from the Student relation. Fig. 8.5 shows the design in 3NF.
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