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CPSC 304 Database Management Systems
Tutorial 5 – Review Session before Midterm I
FDs and Normal Forms
(some questions will be skipped in the tutorial)
Problem 1: Consider a relation R with five attributes ABCDE. You are given the
following dependencies:
A ! B, BC ! E, ED ! A.
1. List all of the candidate keys for R.
2. Is R in 3NF?
3. Is R in BCNF?
Problem 2: Consider the schema with attributes ABCD and FDs:
AB ! C, C ! A, C ! D.
1. Produce a lossless BCNF decomposition for this schema.
2. Is it dependency-preserving? Explain why. If not, produce a dependencypreserving
3NF decomposition.
Problem 3: Suppose you are given a relation R(A,B,C,D). For each of the
following sets of FDs, assuming they are the only dependencies that hold for R,
identify the candidate key(s) for R.
1. B!C, D!A.
2. A!BC, C!AD
3. A!B, B!C, C!D
Problem 4: (Exercise 19.5 of the book) Consider the following collection of
relations and dependencies. Assume that each relation is obtained through
decomposition from a relation with attributes ABCDEFGHI and that all the
known dependencies over relation ABCDEFGHI are listed for each question. (The
questions are independent of each other, obviously, since the given dependencies
over ABCDEFGHI are different.) For each (sub)relation:
(a) State the strongest normal form that the relation is in.
(b) If it is not in BCNF, decompose it into a collection of BCNF relations.
1. R1(A,C,B,D,E), A → B, C → D
2. R2(A,B,F), AC → E, B → F
3. R3(A,D), D → G, G → H
4. R4(D,C,H,G), A → I, I → A
5. R5(A,I,C,E)
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Problem 5: (Exercise 19.7 of the book) Suppose you are given a relation R with
four attributes ABCD. For each of the following sets of FDs, assuming those are
the only dependencies that hold for R, do the following:
(a) Identify the candidate key(s) for R.
(b) Identify the best normal form that R satisfies (3NF, BCNF, or none).
(c) If R is not in BCNF, decompose it into a set of BCNF relations that
preserve the dependencies.
1. C → D, C → A, B → C
2. B → C, D → A
3. ABC → D, D → A
4. A → B, BC → D, A → C
5. AB → C, AB → D, C → A, D → B
RA, DRC and SQL
Problem 6: Consider the following schemas:
Branch (bname, assets, bcity)
Customer (cname, street, ccity)
Deposit (bname, account#, cname, balance)
Borrow (bname, loan#, cname, amount)
Rewrite the English queries below using:
(a) Relational algebra
(b) SQL
1. Find all customers having a loan at the bank and the cities in which they live.
2. Find the largest account balance in the bank.
3. Find all the customers who have an account at all branches located in
Vancouver.
Problem 7: Using the same schemas as in Problem 6, tell what the English
meanings of the following DRC queries are.
1. { < b , l,
c,
a > | < b,
l,
c,
a >∈borrow
∧ a > 1200}
2. { < c > | ∃b,
l,
a(
< b,
l,
c,
a >∈ borrow ∧ a > 1200)}
3. { < c > | ∀x,
y,
z(
¬ ( < x,
y,
z >∈ branch)
∨ z ≠"
Vancouver"
∨(
∃a,
n(
< x,
a,
c,
n >∈ deposit)))}
ER Diagrams and Relational Schema
Problem 8: Consider that the officials in YVR have decided to organize all the
information related to the airport in a DBMS and you have been hired to design
the database. Your first task is to organize the information about the planes
stationed and maintained at the airport. The relevant information is as follows:
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* Every airplane has a registration number and is of a specific model.
* The airport accommodates a number of airplane models and each model is
identified by a model number and has a capacity and a weight.
* A number of technicians work at the airport. You need to store the name, SSN,
address, phone number and salary of each technician.
* Each technician is an expert on one or more plane model(s), and his or her
expertise may overlap with that of other technicians. This information about
technicians must also be recorded.
* Traffic controllers must have an annual medical exam. For each traffic
controller you must store the date of the most recent exam.
* All airport employees (including technicians) belong to a union. You must store
the union membership number of each employee. You can assume that each
employee is uniquely identified by the SSN.
* The airport has a number of tests that are used periodically to ensure that the
planes are still airworthy. Each test has a Federal Aviation Administration
(FAA) test number, a name and a maximum possible score.
* The FAA requires the airport to keep track of each time a given airplane is
tested by a given technician using a given test. For each testing event, the
information needed is the date, the number of hours the technician spent doing
the test, the score the airplane received on the test.
1. Draw an ER diagram for the airport database. Be sure to indicate the various
attributes of each entity and relationship set. Also specify the key and
participation constraints for each relationship set. Specify any necessary overlap
and covering constraints as well.
2. Assume that the tests on a plane must be conducted by technicians who are
expert on that model. How will you express this constraint in the ER model? If
you cannot express it, explain briefly.
3. Translate the ER diagram into a relational schema.
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