Page 610 - Discrete Mathematics and Its Applications

9.2 n-ary Relations and Their Applications 589

TABLE 8 Flights.
Airline Flight_number Gate Destination Departure_time
Nadir 122 34 Detroit 08:10
Acme 221 22 Denver 08:17
Acme 122 33 Anchorage 08:22
Acme 323 34 Honolulu 08:30
Nadir 199 13 Detroit 08:47
Acme 222 22 Denver 09:10
Nadir 322 34 Detroit 09:44

and 09:44. SQL uses the FROM clause to identify the n-ary relation the query is applied to, the
WHERE clause to specify the condition of the selection operation, and the SELECT clause to
specify the projection operation that is to be applied. (Beware: SQL uses SELECT to represent
a projection, rather than a selection operation. This is an unfortunate example of conflicting
terminology.) ▲

Example 13 shows how SQL queries can be made involving more than one table.

EXAMPLE 13 The SQL statement

SELECT Professor, Time
FROM Teaching_assignments, Class_schedule
WHERE Department=’Mathematics’

is used to find the projection P 1,5 of the 5-tuples in the database (shown in Table 7), which
is the join J 2 of the Teaching_assignments and Class_schedule databases in Tables 5 and 6,
respectively, which satisfy the condition: Department = Mathematics. The output would consist
of the single 2-tuple (Rosen, 3:00 p.m.). The SQL FROM clause is used here to find the join of
two different databases. ▲

We have only touched on the basic concepts of relational databases in this section. More
information can be found in [AhUl95].

Exercises

1. List the triples in the relation {(a,b,c) | a, b, and c are 7. The 3-tuples in a 3-ary relation represent the following
integers with 0 <a <b <c < 5}. attributes of a student database: student ID number, name,
2. Which 4-tuples are in the relation {(a,b,c,d) | a, b, c, phone number.
and d are positive integers with abcd = 6}? a) Is student ID number likely to be a primary key?
3. List the 5-tuples in the relation in Table 8. b) Is name likely to be a primary key?
4. Assuming that no new n-tuples are added, find all the
c) Is phone number likely to be a primary key?
primary keys for the relations displayed in
8. The 4-tuples in a 4-ary relation represent these attributes
a) Table 3. b) Table 5.
of published books: title, ISBN, publication date, number
c) Table 6. d) Table 8. of pages.
5. Assuming that no new n-tuples are added, find a compos- a) What is a likely primary key for this relation?
ite key with two fields containing the Airline field for the
database in Table 8. b) Under what conditions would (title, publication date)
be a composite key?
6. Assuming that no new n-tuples are added, find a compos-
ite key with two fields containing the Professor field for c) Under what conditions would (title, number of pages)
the database in Table 7. be a composite key?