The document describes eight relational operators: SELECT, PROJECT, JOIN, INTERSECT, UNION, DIFFERENCE, PRODUCT, and DIVIDE. It provides examples of how each operator manipulates data from one or more tables by selecting, combining, or relating their contents.

1. RELATIONAL SET OPERATORS
Prepared by:
Michelle A. Ogana
Ronnjemmele Rivera
Jane Allyza Catalla
Harry Ochinang
1

2. Relational Set Operators
 This section describes the basic data manipulation
Relational Algebra
 Defines the theoretical way of manipulating table
contents using the eight relational operators.
2

3. Eight Relational Operators
 SELECT
 PROJECT
 JOIN
 INTERSECT
 UNION
 DIFFERENCE
 PRODUCT
 DIVIDE
3

4.  The relational operators have the property of
closure; that is, the use of relational algebra
operators on existing relations (tables) produces
new relations.
 There is no need to examine the mathematical
definitions, properties and characteristics of
those relational algebra operators.
4

5. SELECT
 Also known as RESTRICT
 Yields values for all rows found in a table.
 Used to list all of the row values, or can yield
only those row values that match a specified
criterion.
 SELECT yields a horizontal subset of a table.
5

6. ORIGINAL TABLE
P_CODE P_DESCRIPT PRICE P_CODE P_DESCRIPT PRICE
123456 Flashlight $5.26 123456 Flashlight $5.26
123457 Lamp $25.15 123457 Lamp $25.15
SELECT ALL yields
123458 Box Fan $10.99
123458 Box Fan $10.99
123459 9V Battery $1.29
123459 9V Battery $1.29
254688 100W Bulb $1.47
254688 100W Bulb $1.47
311452 Powerdrill $34.99
311452 Powerdrill $34.99
SELECT only PRICE less than $2.00 yields P_CODE P_DESCRIPT PRICE
123459 9V Battery $1.29
254688 100W Bulb $1.47
SELECT only P_CODE = 311452 yields P_CODE P_DESCRIPT PRICE
311452 Powerdrill $34.99
6

7. PROJECT
 Yields all values for selected attributes.
 It yields a vertical subset of a table.
7

8. ORIGINAL TABLE NEW TABLE
P_CODE P_DESCRIPT PRICE PRICE
123456 Flashlight $5.26
PROJECT PRICE yields $5.26
123457 Lamp $25.15 $25.15
123458 Box Fan $10.99 $10.99
$1.92
123459 9V Battery $1.29
$1.47
254688 100W Bulb $1.47
$34.99
311452 Powerdrill $34.99
P_DESCRIPT PRICE
Flashlight $5.26
Lamp $25.15
PROJECT P_DESCRIPT and PRICE yields Box Fan $10.99
9v battery $1.92
100w bulb $1.47
Powerdrill $34.99
P_CODE PRICE
123456 $5.26
PROJECT P_CODE and PRICE yields 123457 $25.15
123458 $10.99
213345 $1.92
254467 $1.47
311452 $34.99
8

9. UNION
 Combines all rows from two tables, excluding
duplicate rows.
 To be used in UNION, tables must have the same
attribute characteristics
 Columns, and domains must be compatible
 When two or more tables share the same number
of columns, and when their corresponding
columns share the same domains, they are said
to be UNION-COMPATIBLE.
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10. P_CODE P_DESCRIPT PRICE P_CODE P_DESCIPT PRICE
UNION
123456 Flashlight $5.26 345678 Microwave 160.00
123457 Lamp $25.15 345679 Dishwasher 500.00
123458 Box Fan $10.99
123459 9V Battery $1.29
254688 100W Bulb $1.47
yields
311452 Powerdrill $34.99
P_CODE P_DESCRIPT PRICE
123456 Flashlight $5.26
123457 Lamp $25.15
123458 Box Fan $10.99
254688 9V Battery $1.29
524789 100W Bulb $1.47
311452 Powerdrill $34.99
345678 Microwave $ 160
345679 Dishwasher $ 500
10

11. INTERSECT
 Yields only the rows that appear in both
tables.
 As was true in the case of UNION, the tables
must be union-compatible to yield valid
results.
 For example, you cannot use INTERSECT if
one of the attributes is numeric and one is
character-based.
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12. STU_FNAME STU_LNAME EMP_FNAME EMP_LNAME
INTERSECT
George Jones Franklin Lopez
Jane Smith William Turner
Peter Robinson Franklin Johnson
Franklin Johnson Susan Rogers
Martin Lopez
yields
STU_FNAME STU_LNAME
Franklin Johnson
12

13. DIFFERENCE
 Yields all rows in one table that are not found
in the other table;
 It subtracts one table form the other.
 Tables must be union-compatible to yield
valid results.
 Note that subtracting the first table from the
second table is not the same as subtracting
the second table from the first table.
13

14. STU_FNAME STU_LNAME EMP_FNAME EMP_LNAME
DIFFERENCE
George Jones Franklin Lopez
Jane Smith William Turner
Peter Robinson Franklin Johnson
Franklin Johnson Susan Rogers
Martin Lopez
yields
STU_FNAME STU_LNAME
George Jones
Jane Smith
Peter Robinson
Martin Lopez
14

15. PRODUCT
 Yields all possible pairs of rows from two
tables
 Also known as Cartesian product
 Therefore, if one table has six rows and the
other table has three rows,
 The PRODUCT yields a list composed of
6 x 3 = 18 rows
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16. P_CODE P_DESCRIPT PRICE STORE AISLE SHELF
123456 Flashlight $5.26 PRODUCT 23 W 5
123457 Lamp $25.15 24 K 9
123458 Box Fan $10.99 25 Z 6
123459 9V Battery $1.29
254688 100W Bulb $1.47
311452 Powerdrill $34.99 yields
16

17. JOIN
 Allows information to be combined from two
or more tables.
 It is the real power behind the relational
database, allowing the use of independent
tables linked by common attributes
 The CUSTOMER and AGENT tables shown
will be used to illustrate several types of joins.
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18. TABLE name: CUSTOMER TABLE name: AGENT
CUS_CODE CUS_LNAME CUS_ZIP AGENT_CODE AGENT_CODE AGENT_PHONE
1132445 Walker 32145 321 125 6152439887
1217782 Adares 32145 125 167 6153426778
1312243 Rakowski 34129 167 231 6152431124
13212442 Rodriguez 37134 125 333 9041234445
1542311 Smithson 37134 421
1657399 Vanloo 32145 231
18

19.  A natural join links tables by selecting only
the rows with common values in their
common attribute(s).
 It is the result of a three-stage process:
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20. a. First, a PRODUCT of the tables is created
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21. b. Second, a SELECT is performed on the output of Step A to
yield only the rows for which the AGENT_CODE values are equal.
Common columns are referred to as the join columns.
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22. c. A PROJECT is performed on the results of Step B to yield a
single copy of each attribute, thereby eliminating duplicate
columns.
22

23.  The final outcome of a natural join yields a
table that does not include unmatched pairs
and provides only the copies of the matches.
23

24. Note a few crucial features of the natural join operation:
 If no match is made between the table rows, the new table
does not include the unmatched row. In that case, neither
AGENT_CODE 421 nor the customer whose last name is
Smithson is included.
 Smithson’s AGENT_CODE 421 does not match any entry in
the AGENT table.
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25.  The column on which the join was made- that is,
AGENT_CODE- occurs only once in the new table.
 If the same AGENT_CODE were to occur several times in the
AGENT table, a customer would be listed for each match
 For example, if the AGENT_CODE 167 were to occur three
times in the AGENT table, the customer name Rakowski, who
is associated with AGENT_CODE 167, would occur three
times in the resulting table
25

26. Forms of JOIN
1. EQUIJOIN
 Links tables on the basis of an equality
condition that compares specified columns of
each table.
 It does not eliminate duplicate columns
 Condition or criterion used to join the tables
must be explicitly defined.
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27.  Takes its name from the equality comparison
operator (=) used in the condition.
2. Theta Join
 This join is used if any other comparison
operator is used.
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28. 3. Inner Join
 Returns matched records from the tables that
are being joined.
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29. 3. Outer Join
 Matched pairs would be retained, and any
unmatched values in the other table would be
left null.
 Returns all of the matched records that the
inner join returns, plus it returns the
unmatched records from one of the tables
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30. 3.a. Left Outer Join
 Yields all rows in the CUSTOMER table,
including those that do not have a matching
value in the AGENT table.
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31. 3.b. Right Outer Join
 Yields all the rows in the AGENT table,
including those that do not have matching
values in the CUSTOMER table.
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32.  Outer joins operate like equijoins.
 It does not drop one copy of the common
attribute, and it requires the specification of the
join condition.
 Are especially useful when you are trying to
determine what value(s) in related tables
cause(s) referential integrity problems
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33.  You may wonder why the outer joins are
labeled left and right.
 The labels refer to the order in which the
tables are listed in the SQL command.
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34. DIVIDE
 Uses one single-column table (e.g., column “a”) as
the divisor and one 2-column table (i.e., columns “a”
and “b”) as the dividend.
 The tables must have common column
 Single column with the values of column “a” from
the dividend table rows where the value of the
common column (i.e., column “a” ) in both tables.
34

35. CODE LOC CODE LOC
DIVIDE
A 5 A 5
B
A 9
A 4 yields
B 5
B 3
C 6
D 7 A. Table 1 is divided by Table 2 to produce Table 3.
D 8
Tables 1 & 2 both contain the column CODE but
E 8
do not share LOC.
B. To be included in the resulting Table 3, a value in the
unshared column (LOC( must be associated (in the dividing
Table 2) with every value in Table 1.
C. The only value associated with both A and B is 5.
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36. 36