Relational AlgebraRelational Calculus

Objectives Fundamental operations in RA Union Set difference Select Project Cartesian Product Relational Calculus

Chapter Five

2

Query Languages

1. Procedural Relational Algebra (RA)

2. Non-Procedural Tuple Relational Calculus Domain Relational Calculus

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Fundamental Operations in RA Binary Operations

UNION MINUS CARTESIAN PRODUCT

Unary Operations SELECT PROJECT

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Union of R S

1. Union of R Sa. All tuples in R or Sb. Union Compatible

Some degree Attributes of R&S must be the same

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Union of R S

Faculty Name

ID Salary

Smith 1 70,000

Nelson

3 85,000

Larson

6 62,000

Staff Name ID Salary

Smith 1 70,000

Anderson 3 45,000

Faculty U Staff

Name ID Salary

Smith 1 70,000

Nelson 3 85,000

Larson 6 62,000

Anderson 3 45,000

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Union of R S

name (faculty) name (staff)

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Set Difference (MINUS) R - S Set of tuples in R but not in S Union Compatible

Faculty - Staff

Name ID Salary

Nelson 3 85,000

Larson 6 62,000

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Intersection: R S Set of of tuples belong to both R & S Union CompatibleFind the list of faculty members who are also

staff

70,0001Smith

SalaryIDNameFaculty Staff

R S = R – (R – S)

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Cartesian Product R x S Set of (K1 + K2) tuples: The first K1 tuples are

from R. The last K2 tuples are from S

Semester

S_Num

Year Season

1 99 F

2 99 S

3 00 FSemester_Course

C_Num S_Num

200 1

250 1

300 2

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Cartesian Product R x SRxS S_Num Year Season C_Num S_Num

1 99 F 200 1

1 99 F 250 1

1 99 F 300 2

2 99 S 200 1

2 99 S 250 1

2 99 S 300 2

3 00 F 200 1

3 00 F 250 1

3 00 F 300 2

List of courses offered in year 99?

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Selection (Unary Relation) Select tuples that satisfy a given

predicate major = ‘COSC’ (Student)

Result is another relation Conditions are relational operator

(,, , , ) Logical operators AND (), OR(),

NOT()

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Selection (Unary Relation) Find all Faculty members which make

less than $45,000 salary < 45,000(Faculty)

Find all staff who make less than $40,000 and ID > 100

salary < 40,000 AND ID > 100 (Staff) List of number of courses offered in year

99 S_Num = S_Num AND year = 99 (Semester x

Semester_Course)

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Projection (Unary) Select attributes (Pi) Find the number of faculty that

teach COSC courses name( course=‘COSC’(Faculty))

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R S Theta join allows us to combine the selection & the

cartesian product into an operation

Theta Join

R A B

a b

B c

b c

R C D E

a b c

a b d

b e c

a c d

R S A B C D E

a b a b c

a b a b d

a c a c d

b c a c d

If is = It is called EquijoinIf the attributes have the same name, the join is called Natural Join

DB

ji

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Relational Calculus (RC)

Non-procedural Most commercial query language Types:

Tuple RC: Variables represent tuples Domain RC: Variables represent

values of domain

Part Two

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Tuple Relational Calculus:{ t | P(t)}

Examples List of students with GPA > 3 { t | t Є student ^ t[GPA] > 3 } List of students name with GPA > 3 { t | s Є student (t[NAME] = s[NAME]

^ t[GPA] > 3)}