Analysis and Design of Data Systems. Relational Algebra 2 (Lecture 18)

Сентябрь 7, 2022

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Analysis and Design of Data Systems. Relational Algebra 2 (Lecture 18)

Содержание

2. A B A B A B UNION MINUS INTERSECTION Set Operations UNION, INTERSECTION, MINUS The next
3. Set Operations UNION, INTERSECTION, MINUS UNION, INTERSECTION, and MINUS are binary operations. This means that the
4. UNION Example: Retrieve the Social Security numbers of all employees who either work in department 5
5. Set operations (attributes naming)
6. CARTESIAN PRODUCT Operation (CROSS PRODUCT) Cartesian product operation produces a new element by combining every tuple
7. CARTESIAN PRODUCT Operation Example: retrieve a list of names of each female employee’s dependents Step 1:
8. CARTESIAN PRODUCT Operation Step 2: Step 3:
9. CARTESIAN PRODUCT Operation Step 4: Step 5: Because this sequence of CARTESIAN PRODUCT followed by SELECT
10. Example: retrieve the name of the manager of each department. SELECT d.Dname, e.Fname, e.Lname FROM EMPLOYEE
11. where is of the form: AND AND … AND (condition)
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A B
A B
A B
UNION
MINUS
INTERSECTION
Set Operations UNION, INTERSECTION, MINUS
The next group of relational

algebra operations are the standard mathematical operations on sets.

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Set Operations UNION, INTERSECTION, MINUS
UNION, INTERSECTION, and MINUS are binary operations.

This means

that the two relations have the same number of attributes and each corresponding pair of attributes has the same domain.

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UNION
Example: Retrieve the Social Security numbers of all employees who either

work in department 5 or directly supervise an employee who works in department 5.

Step 1:

Step 2:

Step 3:

Step 4:

or, as a single relational algebra expression:

Set operations eliminate duplicates

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Set operations (attributes naming)

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CARTESIAN PRODUCT Operation (CROSS PRODUCT)

Cartesian product operation produces a new element by

combining every tuple from one relation with every tuple from the other relation.

The CARTESIAN PRODUCT operation by itself is generally meaningless, except when followed by a selection that matches values of attributes coming from the component relations.

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CARTESIAN PRODUCT Operation
Example: retrieve a list of names of each female

employee’s dependents

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Step 1:

Resulting Relations:

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CARTESIAN PRODUCT Operation
Step 2:
Step 3:

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CARTESIAN PRODUCT Operation
Step 4:
Step 5:
Because this sequence of CARTESIAN PRODUCT followed

by SELECT is quite commonly used to combine related tuples from two relations, a special operation, called JOIN, was created to specify this sequence as a single operation.

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Example: retrieve the name of the manager of each department.
SELECT d.Dname,

e.Fname, e.Lname
FROM EMPLOYEE e, DEPARTMENT d
WHERE Ssn = Mgr_ssn;

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where is of the form:
AND AND

… AND (condition)