1. Binary Operations in Relational Algebra & SQL

2. Set Based: UNION, INTERSECTION, DIFFERENCE

3. UNION operation Example SQL for previous example Fig 6.4:
Suppose names of people are distinct A
RESULT=STUDENT INSTRUCTOR B
SQL for previous example Fig 6.4:
(SELECT Fn, Ln FROM STUDENT)
UNION
(SELECT Fname, Lname FROM INSTRUCTOR);

4. Union Compatibility Requirement for the traditional set operators
Strong requirement
Same number of columns
Each corresponding column is compatible
Positional correspondence
How are rows compared?
- Chapter 3 material: present again for review if desired
- Can instead present material in Chapter 4 and skip when initially covering chapter 3
- Join: compares rows on the join column(s)
- Traditional set operators compare on all columns
Strong requirement:
- Usually on identical tables (geographically dispersed tables)
- Compatible columns: data types are comparable (numbers cannot be compared
to strings)
- Positional: 1st column of table A to 1st column of table B, 2nd column etc
Can be applied to similar tables (faculty and student) by removing columns before traditional set operator

5. INTERSECTION operation
Example
Suppose names of people are distinct A B
RESULT=STUDENT INSTRUCTOR
SQL for previous example Fig 6.4:
(SELECT Fn, Ln FROM STUDENT)
INTERSECT
(SELECT Fname, Lname FROM INSTRUCTOR);

6. SET DIFFERENCE operation
Example
STUDENT - INSTRUCTOR
INSTRUCTOR - STUDENT
Suppose names of people are distinct
(d) RESULT=INSTRUCTOR - STUDENT A B
(e) RESULT=STUDENT - INSTRUCTOR B
SQL for previous example Fig 6.4:
(SELECT Fn, Ln FROM STUDENT)
MINUS
(SELECT Fname, Lname FROM INSTRUCTOR);

7. CARTESIAN PRODUCT operation
Example B
Relational Algebra: RESULT= Faculty ✕ Student
SQL: SELECT * FROM Faculty, Student;

8. EQUI-Join
EQUI-Join
EQUI-Join
Example:
RESULT= Faculty (Faculty.FacSSM=Offering.FacSSN)Offering;
SELECT *
FROM Faculty, Offering
WHERE Faculty.FacSSN=Offering.FacSSN;

9. Exercise 1 for Equi-Join
SQL query Result
T (T1.P=T2.A)T2
T (T1.Q=T2.B)T2

10. NATURAL-Join Example: RESULT= Faculty * Offering; SELECT *
FROM EMPLOYEE NATURAL JOIN DEPARTMENT

11. THETA Join Example: RESULT=Car {CarPrice>BoatPrice} Boat;
Result=R1 {Condition} R2; Condition: {<, >, =, ≤, ≥, ≠};
EquiJoin when “=“.
SELECT * FROM Car, Boat
WHERE CarPrice>BoatPrice;

12. THETA Join Example: SELECT * FROM Faculty, Offering
EQUI-Join
Example:
SELECT * FROM Faculty, Offering
WHERE Faculty.FacSSM=Offering.FacSSN;

13. Exercise 2 Department Student Faculty
Dno
Dname
DHeadSsn
Location
SID
Sname
Dno
SAge
Student
FSsn
Fname
Dno
FAge
Faculty
Write Relational Algebra and SQL queries for following questions:
What are the names of students who are from department ‘Computer Science’?
What are the names of faculties who are younger than a student?
What are the names of faculties who works in ‘Keller Hall’?

14. Summary Binary Operation Operation from Set Theory Join Operation
UNION
INTERSECTION
DIFFERENCE
CARTESIAN PRODUCT
Join Operation
Equi-Join
Natural Join
Theta Join

15. Reference
Materials in the slides are from Elmasri, Navathe, Fundamentals of Database Systems, 6th, Addison Wesley and Michael V. Mannino, Database: Design, Application Development & Administration, Third Edition, McGraw Hill