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the pair of MVDs X →→ Y | Z (defined with respect to heading H , where H is equal to the union of X , Y , and Z ),
then X →→ Y is trivial if and only if X →→ Z is trivial.
The following rule of thumb is often adopted in practice:
Let relvar R have heading H and let the heading H of R be partitioned into disjoint subsets X , Y , and Z . Further, let X be
the sole key and let Y and Z both be relation valued. Then, using Heath notation once again, R should be replaced by R1
and R2 , where R1 = ( R { XY }) UNGROUP ( Y ) and R2 = ( R { XZ }) UNGROUP ( Z ), respectively. Note: UNGROUP is an
operator of Tutorial D . I used it in the answer to Exercise 4.14 in Appendix D. It's discussed in detail in SQL and
Relational Theory and elsewhere.
How does this rule of thumb relate to the topics discussed in the present chapter?
12.9 ( Modified version of Exercise 9.3 .) Design a database for the following. The entities to be represented are
sales representatives, sales areas, and products. Each representative is responsible for sales in one or more areas;
each area has one or more responsible representatives. Each representative is responsible for sales of one or more
products, and each product has one or more responsible representatives. Each product is sold in each area; however,
no two representatives sell the same product in the same area. Each representative sells the same set of products in
each area for which that representative is responsible.
12.10 The following dependencies are defined with respect to a heading consisting of attributes ABCD :
A →→ B | C
Use the chase to show these dependencies imply the MVDs A →→ C | D. Note: I'm making use of a certain
shorthand notation here, according to which A →→ B | C and A →→ C | D denote, respectively, A →→ B | CD and
A →→ C | DB . See the answer to the exercise in Appendix D for further explanation.
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