190
Chapter 19
3. Consider the set of FD:
AB
→
CD
and
B
→
C
.
AB
is obviously a key for this
relation since
AB
→
CD
implies
AB
→
ABCD
. It is a primary key since there are
no smaller subsets of keys that hold over
R(A,B,C,D)
. The FD:
B
→
C
violates
2NF since:
C
∈
B
is false; that is, it
is not
a trivial FD
B is not
a superkey
C is not
part of some key for
R
B is
a proper subset of the key
AB
(transitive dependency)
4. Consider the set of FD:
AB
→
CD
and
C
→
D
.
AB
is obviously a key for this
relation since
AB
→
CD
implies
AB
→
ABCD
. It is a primary key since there are
no smaller subsets of keys that hold over
R(A,B,C,D)
. The FD:
C
→
D
violates
3NF but not 2NF since:
D
∈
C
is false; that is, it
is not
a trivial FD
C is not
a superkey
D is not
part of some key for
R
5. The only way
R
could be in BCNF is if
B
includes a key,
i.e. B
is a key for R.
6. It means that the relationship is one to one. That is, each A entity corresponds
to at most one
B
entity and viceversa. (In addition, we have the dependency
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 Fall '12
 Dr.Vishak
 Database normalization, relation, BCNF

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