Databases Reference
In-Depth Information
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?
