Discrete Mathematics for Computer Science

Relational Databases: An Introduction 201

Table 3.17 Registration' Relation

Registration'

Student Department

John von Neumann English

Emmy Noether English

Herman Hollerith English

George Boole English

Ren6 Descartes English

Winston Churchill English

George Boole Mathematics

Winston Churchill Mathematics

Ren6 Descartes Computer Science

Herman Hollerith Computer Science

Example 1. Projection is actually a common operation in areas other than databases.
Look at graphing relations on R^2 , and consider the relation

C = {(x, y) E R2 : (x - 2)^2 + (y -2)2 = 1}

The graph of C is a circle in the plane with center (2, 2) and radius 1. Figure 3.19 shows
the graph of C and its projection onto the x-axis.

(2, 3)

3

2 (1,2) 9(2,2) (3,2)

(2, 1)

1

3

Figure 3.19 The projection of the circle (x - 2)2 + (y - 2)2 = 1 onto the x-axis.

Two values or points on the circle are projected onto each element in the open interval

(1,3).

Third Operation: Join

Consider two relations, such as Registration and TeachingAssignments. Recall it was ar-
gued that since they really store different information, they need to be two separate tables.
Nevertheless, some people using the system will want to know the combined information-
that is, which students are taking which classes (departments, course numbers, and section
numbers) taught by which professors. The join of the two relations puts all the information
together. The relation that is needed, called JoinedRelation, is shown in Table 3.18. The