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Database Management Systems (CIS 4301)
(Spring 2008)
Instructor: Dr. Markus Schneider
TAs:
Ganesh Viswanathan
Wenjie Yuan
Homework 4
Solution
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Exercise 1
16
Exercise 2
24
Exercise 3.1
15
Exercise 3.2
15
Exercise 3.3
30
Total
100
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View Full Document Exercise 1 (Knowledge Questions) [16 points]
Answer the following questions.
1. What is “functional” about functional dependencies? [2 points]
Let r be the relation schema of a relation R, and let A, B
⊆
R. B is functionally
dependent on A, or A determines B functionally (uniquely), written A
→
B if,
and only if, to each value in A exactly one value in B belongs:
A
→
B
⇔
∀
t1, t2
∈
R : t1[A] = t2[A]
⇒
t1[B] = t2[B]
for all possible relations R over r.
We can see that in principle, there is a function A
→
B that produces a set of
value B according to a set of value A. This is “functional” about function
dependencies.
2. What are Armstrong's Axioms for reasoning with a set of functional dependencies?
[3 points]
Let R be a relation schema, F a set of FDs and A, B, C
⊆
R.
The following inference rules are used to compute F
+
(Armstrong’s axioms):
−
reflexivity rule: Let B
⊆
A. Then always A
→
B (special case: A
→
A)
holds.
−
augmentation rule: If A
→
B holds, then also A
∪
C
→
B
∪
C holds.
−
transitivity rule: If A
→
B and B
→
C holds, then also A
→
C holds.
3. What are the goals of designing a good relation schema? [3 points]
Solution:
avoidance of redundancy and anomalies
avoidance of information loss
4. What is meant by the closure of a set of functional dependencies? [2 points]
F
+
is called the closure of F, means F
+
is the set of all FDs that can be logically
implied from the FDs in F.
5. What is the difference between a key and a super key? [2 points]
The difference between a key and a superkey is that a key has to be minimal; that
is , if we have a key K={A1, A2, …,An} of R, then k{Ai} is not a key of R for
any Ai
∈
K.
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This note was uploaded on 09/10/2008 for the course CIS 4301 taught by Professor Schneider during the Spring '08 term at University of Florida.
 Spring '08
 Schneider
 Databases

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