Database Modeling and Design

6.5 Fourth and Fifth Normal Forms 135
posed into three tables, A->B, A->C, and A->D, all based on the same
superkey A; however, it is already in 5NF without the decomposition.
Thus, the decomposition is not required for normalization. On the other
hand, decomposition can be a useful tool in some instances for performance
improvement.
The following example demonstrates that a table representing a ternary
relationship may not have any two-way lossless decompositions;
however, it may have a three-way lossless decomposition, which is
equivalent to three binary relationships, based on the three possible projections
of this table. This situation occurs in the relationship skill-incommon
(Figure 6.6), which is defined as “The employee must apply the
intersection of his or her available skills with the skills needed to work
on certain projects.” In this example, skill-in-common is less restrictive
than skill-required because it allows an employee to work on a project
even if he or she does not have all the skills required for that project.
As Table 6.6 shows, the three projections of skill_in_common
result in a three-way lossless decomposition. There are no two-way lossless
decompositions and no MVDs; thus, the table skill_in_common is
in 4NF.
The ternary relationship in Figure 6.6 can be interpreted yet another
way. The meaning of the relationship skill-used is “We can selectively
record different skills that each employee applies to working on individual
projects.” It is equivalent to a table in 5NF that cannot be decomposed
into either two or three binary tables. Note by studying Table 6.7
that the associated table, skill_used, has no MVDs or JDs.
Table 6.7
The Table skill_used, Its Three Projections, and Natural Joins of
Its Projections
skill_used emp_id proj_no skill_type
101 3 A
101 3 B
101 4 A
101 4 C
102 3 A
102 3 B
102 4 A
102 4 B