1. Relational Algebra Relational Calculus
Chapter Five
Objectives
Fundamental operations in RA
Union
Set difference
Select
Project
Cartesian Product
Relational Calculus
COSC 640 Chapter 5

2. Query Languages Procedural Non-Procedural Relational Algebra (RA)
Tuple Relational Calculus
Domain Relational Calculus

3. Fundamental Operations in RA
Binary Operations
UNION
MINUS
CARTESIAN PRODUCT
Unary Operations
SELECT
PROJECT

4. Union of R  S Union of R  S All tuples in R or S Union Compatible
Some degree
Attributes of R&S must be the same

5. 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
45,000

6. name (faculty)  name (staff)
Union of R  S
name (faculty)  name (staff)

7. 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

8. Intersection: R  S Set of of tuples belong to both R & S
Union Compatible
Find the list of faculty members who are also staff
70,000 1
Smith
Salary ID
Name
Faculty  Staff
R  S = R – (R – S)

9. 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 S 3 00
Semester_Course
C_Num
S_Num
200 1
250
300 2

10. Cartesian Product R x S List of courses offered in year 99? RxS S_Num
Season
C_Num 1 99 F
200
250
300 2 S 3 00
List of courses offered in year 99?

11. 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()

12. 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)

13. Projection (Unary) Select attributes (Pi)
Find the number of faculty that teach COSC courses
name( course=‘COSC’(Faculty))

14. Theta Join
R S
Theta join allows us to combine the selection & the cartesian product into an operation R A B a b c R C D E a b c d e
R S A B C D E a b c d
If  is = It is called Equijoin
If the attributes have the same name, the join is called Natural Join

15. Relational Calculus (RC)
Part Two
Relational Calculus (RC)
Non-procedural
Most commercial query language
Types:
Tuple RC: Variables represent tuples
Domain RC: Variables represent values of domain

16. 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)}