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CHAPTER 3 Relations
INPUT: Relations R and S with common attributes B 1 , B 2.
Bj
OUTPUT: Relation J that is the join of R and S on B 1 , B 2.
Bj
J=0
for each tuple x E R do
Select all tuples y c S whose values on B 1.
Bj
are all the same as x's
for each such tuple y do
Form a tuple z by concatenating x with y
Eliminate the duplicate entries for attributes
B 1 , B 2.
Bj, creating a tuple z'
J = J U {Z')
Example 3. Use relational algebra, applied to the relations Registration and TeachingAssignments, to find a list of all professors who have either Ren6 Descartes or Winston
Churchill as students.
Solution. First, form the natural join of Registration and TeachingAssignments. Then,
select all tuples in the joined relation with student Ren6 Descartes or Winston Churchill.
The result is shown in Table 3.19.
Table 3.19 Step lJoin
Step l Join
Student
Department
Course Section
Professor
Ren6 Descartes
English
101
4
William Morris
Winston Churchill English
101
4
William Morris
Winston Churchill Mathematics
101
1
David Hilbert
Winston Churchill Mathematics
101
1
Leonardo of Pisa
Ren6 Descartes
Computer Science 103
3
Alan Turing
Finally, project the SteplJoin relation onto the attribute set {Professorl, and remove
any duplicate entries. The resulting relation is shown in Table 3.20.
The relation Professor answers the question of which professors have either Winston
Churchill or Ren6 Descartes as a student.
0