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# Kroenke Ch2 Solutions Essay

1381 words - 6 pages

Chapter 3 and 4 and Relational Algebra

Chapter 3:

1. Consider the relation (20 points):
PERSON_2 (Name, Sibling, Shoe_Size, Hobby)
Assume that the following functional dependencies exist:
Name  Sibling
Name  Shoe_Size
Name  Hobby

a. Describe deletion, modification, and insertion anomalies for this relation.
Consider the following relation:
Name Sibling Shoe_Size Hobby
Jones Fred E Model boats
Jones Fred E Scuba Diving
Jones Sally E Model boats
Jones Sally E Scuba Diving
Jones Frank E Model boats
Jones Frank E Scuba Diving
Greene Nikki B Embroidery
Chau Jonathan C Scuba diving
Chau Eileen C Scuba diving

Deletion anomaly:
If a Name drops a Hobby, one line ...view middle of the document...

2. Consider the relation (50 points):
STUDENT (Number, Name, Dorm, RoomType, DormCost, Sibling, Nickname)
Assume that students pay different dorm costs, depending on the type of room they have. Assume that students can have multiple nicknames.
a. State any multivalued dependencies.
We will assume that Number  Name where name is not unique (i.e., there may be more than one “John Smith”, each with a different student number). Then the multivalued dependencies are:
Number  Sibling
Number  Nickname
Note: We can not assume that Name  Nickname because Name is not unique. For example, one John Smith may have the nickname “Johnny” while another John Smith has the nickname “Joe”. If Name  Nickname then John Smith  (“Johnny”, “Joe”) which means that both nicknames apply to both John Smiths. But this is not the case – each John Smith has only one nickname, and they are not the same.
b. State the functional dependencies.
We will assume that Number  Name where name is not unique (i.e., there may be more than one “John Smith”, each with a different student number). Then the functional dependencies are:
Number  Name
Number  Dorm
Number  RoomType
RoomType  DormCost
Note: This assumes that only RoomType  DormCost – that is, the cost of a certain type of dorm room is the same no matter what dorm the student is living in. An alternate assumption would be that (Dorm, RoomType)  DormCost, where the cost of the type of dorm room varies form dorm to dorm.
c. Transform this table into two or more tables such that each table is in BCNF and in 4NF. State the primary keys, candidate keys, foreign keys, and referential integrity constraints.
We’ll move the obvious multivalued dependencies into their own tables, and then check for BCNF. IF we have BCNF and no multivalued dependencies, we also have 4NF:
STEP ONE: MOVE MUTIVALUED DEPENDENCIES INTO SEPARATE TABLES:
STUDENT_2 (Number, Name, Dorm, RoomType, DormCost)
STUDENT_SIBLING (Number, Sibling)
STUDENT_NICKNAME (Number, Nickname)
STEP TWO: CHECK EACH OF THE RESULTING TABLES FOR BNCF:
STEP TWO (A): CHECK STUDENT
STUDENT_2 FUNCTIONAL DEPENDENCIES:
STUDENT_2 (Number, Name, Dorm, RoomType, DormCost)
Number  Name
Number  Dorm
Number  RoomType
RoomType  DormCost
STUDENT_2 CANDIDATE KEYS:
Number
Is every determinant a candidate key?
NO, RoomType is NOT a candidate key.
Therefore the relation is NOT in BCNF.
Therefore, move RoomType  DormCost into another table
STUDENT_3 (Number, Name, Dorm, RoomType)
DORM_RATE (RoomType, DormCost)
STEP TWO (A) (1): CHECK STUDENT_3:
STUDENT FUNCTIONAL DEPENDENCIES:
STUDENT_3 (Number, Name, Dorm, RoomType)
Number  Name
Number  Dorm
Number  RoomType
STUDENT CANDIDATE KEYS:
Number
Is every determinant a candidate key?
YES, Therefore STUDENT_3 is in BNCF.
STEP TWO (A) (2): CHECK STUDENT:
DORM_RATE FUNCTIONAL DEPENDENCIES:
DORM_RATE (RoomType, DormCost)
...

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