Discrete Mathematics for Computer Science

206 CHAPTER 3 Relations

(that is, some Ri), the (name of the) attribute on which the selection is to be made, and a

finite set of possible values for that attribute. Then, the database system outputs all tuples

in that relation with a value for the attribute that is in that finite set.

There is also a second form that we shall use in the exercises: The user may input the

name of the relation, the names of two attributes, and = or <. If the user inputs Teaching-

Assignments, Section, Course, and <, then the user is asking for all scheduled courses

(for which teachers have been assigned) where the section number is less than the course

number.

What we have given here is a much more limited than the standard database definition

of selection. We have adopted this definition to keep the exposition simple.

Second Operation: Projection

For any table in a relational database, it often happens that a query is only interested in one

attribute. For example, in the relation R' in Table 3.14, suppose that you want to know the

names of the students. The only attribute of interest is Student. The attributes Department,

Course, and Section all may be important in other contexts, but for now, only the Student

entries are needed. The operation that reduces a relation to a new relation consisting of

some of the attributes and the entries for those attributes is called projection.

The second operation, or projection, is now used to find a relation that consists of

some of the attributes of an existing relation. A relation, such as Registration, and a subset

of its attributes, such as {Student, Department, I form the projection Rt of the relation onto

those attributes as follows: First, delete the attributes not in {Student, Department} from

each tuple of the relation Registration. The resulting relation Rt is shown in Table 3.16.

Table 3.16 Rt Relation with Duplicates

Rt

Student Department

John von Neumann English ÷-

Emmy Noether English

Herman Hollerith English

George Boole English

Ren6 Descartes English

Winston Churchill English

John von Neumann English +-

Emmy Noether English

George Boole Mathematics

Winston Churchill Mathematics

Ren6 Descartes Computer Science

Herman Hollerith Computer Science

In Table 3.16, you see that the tuples (John von Neumann, English) and (Emmy

Noether, English) occur twice. Since a relation is a set, it makes no sense to say twice

that a tuple is an element of a set. So, the final step in forming a projection is to eliminate

duplicate entries from the table Rt to form the relation Registration' shown in Table 3.17.

The projection of Registration tells which students are taking classes in which depart-

ments.