Which of the following can lead to partial dependencies

CHAPTER 10: FUNCTIONAL DEPENDENCIES AND NORMALIZATION FOR RELATIONAL DATABASES

Answers to Selected Exercises

15.19 Suppose we have the following requirements for a university database that is

used to keep track of students transcripts:

(a) The university keeps track of each student's name (SNAME), student number

(SNUM), social security number (SSSN), current address (SCADDR) and phone

(SCPHONE), permanent address (SPADDR) and phone (SPPHONE), birthdate

(BDATE), sex (SEX), class (CLASS) (freshman, sophomore, ..., graduate),

major department (MAJORDEPTCODE), minor department (MINORDEPTCODE)

(if any), and degree program (PROG) (B.A., B.S., ..., Ph.D.). Both ssn and

student number have unique values for each student.

(b) Each department is described by a name (DEPTNAME), department code

(DEPTCODE), office number (DEPTOFFICE), office phone (DEPTPHONE), and

college (DEPTCOLLEGE). Both name and code have unique values for each

department.

(c) Each course has a course name (CNAME), description (CDESC), code number

(CNUM), number of semester hours (CREDIT), level (LEVEL), and offering

department (CDEPT). The value of code number is unique for each course.

(d) Each section has an instructor (INSTUCTORNAME), semester (SEMESTER), year

(YEAR), course (SECCOURSE), and section number (SECNUM). Section numbers

distinguish different sections of the same course that are taught during the same

semester/year; its values are 1, 2, 3, ...; up to the number of sections taught

during each semester.

(e) A transcript refers to a student (SSSN), refers to a particular section, and

grade (GRADE).

Design an relational database schema for this database application. First show all

the functional dependencies that should hold among the attributes. Then, design

relation schemas for the database that are each in 3NF or BCNF. Specify the key

attributes of each relation. Note any unspecified requirements, and make

appropriate assumptions to make the specification complete.

10.18 Prove or disprove the following inference rules for functional dependencies. A

proof can be made either by a proof argument or by using inference rules IR1 through IR3. A disproof should be done by demonstrating a relation instance that satisfies the conditions and functional dependencies in the left hand side of the inference rule but do not

satisfy the conditions or dependencies in the right hand side.

(a) {W ->Y, X ->Z} |= {WX ->Y }

(b) {X ->Y} and Z subset-of Y |= { X ->Z }

(c) { X ->Y, X ->W, WY ->Z} |= {X ->Z}

(d) {XY ->Z, Y ->W} |= {XW ->Z}

(e) {X ->Z, Y ->Z} |= {X ->Y}

(f) {X ->Y, XY ->Z} |= {X ->Z}

10.19 Consider the following two sets of functional dependencies F= {A ->C, AC ->D,

E ->AD, E ->H} and G = {A ->CD, E ->AH}. Check whether or not they are

equivalent.

10.22 What update anomalies occur in the EMP_PROJ and EMP_DEPT relations of

Figure 14.3 and 14.4?

10.23 In what normal form is the LOTS relation schema in Figure 10.11(a) with the

respect to the restrictive interpretations of normal form that take only the

primary key into account? Will it be in the same normal form if the general

definitions of normal form were used?

Answer:

If we only take the primary key into account, the LOTS relation schema in Figure 14.11

(a) will be in 2NF since there are no partial dependencies on the primary key .

However, it is not in 3NF, since there are the following two transitive dependencies on

the primary key:

PROPERTY_ID# ->COUNTY_NAME ->TAX_RATE, and

PROPERTY_ID# ->AREA ->PRICE.

Now, if we take all keys into account and use the general definition of 2NF and 3NF, the

LOTS relation schema will only be in 1NF because there is a partial dependency

COUNTY_NAME ->TAX_RATE on the secondary key {COUNTY_NAME, LOT#}, which

violates 2NF.

10.24 Prove that any relation schema with two attributes is in BCNF.

10.25 Why do spurious tuples occur in the result of joining the EMP_PROJ1 and

EMPLOCS relations of Figure 14.5 (result shown in Figure 14.6)?

10.26 Consider the universal relation R = {A, B, C, D, E, F, G, H, I} and the set of

functional dependencies F = { {A, B} -> {C}, {A} -> {D, E}, {B} -> {F}, {F} ->

{G, H}, {D} -> {I, J} }. What is the key for R? Decompose R into 2NF, then 3NF

relations.

10.27 Repeat exercise 10.26 for the following different set of functional dependencies

G = { {A, B} -> {C}, {B, D} -> {E, F}, {A, D} -> {G, H}, {A} -> {I}, {H} -> {J} }.

14.26, starting with the following relation R:

R = {A, B, D, C, E, F, G, H, I}

The first-level partial dependencies on the key (which violate 2NF) are:

{A, B} -> {C, I}, {B, D} -> {E, F}, {A, D}+ -> {G, H, I, J}

Hence, R is decomposed into R1, R2, R3, R4 (keys are underlined):

R1 = {A, B, C, I}, R2 = {B, D, E, F}, R3 = {A, D, G, H, I, J}, R4 = {A, B, D}

Additional partial dependencies exist in R1 and R3 because {A} -> {I}. Hence, we remove

{I} into R5, so the following relations are the result of 2NF decomposition:

R1 = {A, B, C}, R2 = {B, D, E, F}, R3 = {A, D, G, H, J}, R4 = {A, B, D}, R5 = {A, I}

Next, we check for transitive dependencies in each of the relations (which violate 3NF).

Only R3 has a transitive dependency {A, D} -> {H} -> {J}, so it is decomposed into R31

and R32 as follows:

R31 = {H, J}, R32 = {A, D, G, H}

The final set of 3NF relations is {R1, R2, R31, R32, R4, R5}