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b.
Does the set of FDs { C D , B C } imply the JD { AB , BC , CD }?
c.
Does the set of FDs { A B , B C } imply the JD { AB , BC , CD }?
d.
Does the the JD { BC , ABD } imply the JD { AB , BC , CD }?
11.3 We know from Exercise 5.4 that the converse of Heath's Theorem is false. However, there's an extended
version of that theorem whose converse is true. Here it is:
Heath's Theorem ( extended version ): Let relvar R have heading H and let X , Y , and Z be subsets of H such
that the union of X , Y , and Z is equal to H . Let XY denote the union of X and Y , and similarly for XZ . If R is
subject to the FD X Y , then (a) R is subject to the JD { XY , XZ }, and (b) XZ is a superkey for R .
Prove part (b) of this theorem. Prove also that (a) and (b) together imply that X Y holds (the converse of the
extended theorem).
11.4
Consider the following JDs, both of which hold in relvar S:
{ { SNO , SNAME , CITY } , { CITY , STATUS } , { SNAME , CITY } }
{ { SNO , SNAME , CITY } , { CITY , STATUS , SNAME } }
I pointed out in the body of the chapter (in the section “Combining Components”) that although the first of these JDs
implied the second, decomposing relvar S on the basis of that second JD (even though it's irreducible) wouldn't be a
good idea. Why not?

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