Relational Databases: An Introduction
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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 argued 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 informationthat 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