2. The Relational Algebra:
Relational algebra is the basic set of operations for the
relational model
These operations enable a user to specify basic retrieval
requests (or queries)
The result of an operation is a new relation, which may
have been formed from one or more input relations
3. The fundamental operations in the
relational algebra:
Unary operations: are called unary operations, because they operate on
one relation.
▫Select.
▫Project.
Binary operations: operate on pairs of relations and are, therefore, called
binary operations.
▫Union.
▫Intersection
▫set difference.
▫Cartesian product.
4. 1- The Select Operation
The select operation selects tuples that satisfy a given
predicate.
We use the lowercase Greek letter sigma (Ϭ) to denote
selection
In general, the SELECT operation is denoted by
σ<selection condition>(R)
5. To select tuples of the instructor relation where the instructor is in the “Physics”
department, we write:
Ϭ dept_name =“Physics” (instructor )
•The Result will be
9. 3- The Union Operation
For a union operation r ∪ s to be valid, these two conditions must be
hold:
The relations r and s must have the same number of attributes.
The domains of the ith attribute of r and the ith attribute of s must be
the same, for all i.
10.
11.
12.
13.
14. 4- The Intersection:
Intersection is denoted by ∩
The result of this operation, denoted by R ∩ S, is a
relation that includes all tuples that are in both R and S.
The attribute names in the result will be the same as the
attribute names in R
The two operand relations R and S must be “type
compatible”
15. 5- The Set-Difference Operation
The set-difference operation, denoted by (−)
allows us to find tuples that are in one relation but are
not in another.
The expression r − s produces a relation containing those
tuples in r but not in s.
16.
17. 6- The Cartesian-Product Operation
denoted by a cross (×).
allows us to combine information from any two relations.
We write the Cartesian product of relations r1 and r2 as r1
× r2.
25. Binary Relational Operations: Outer JOIN
Operation
The outer-join operation is an extension of the join
operation to deal with missing information.
Some tuples in either or both of the relations being joined
may be lost.
The outer join operation works in a manner similar to the
natural join operation but preserves those tuples that
would be lost in an join.
This is done by creating tuples in the result containing null
values.
26. Binary Relational Operations: Outer JOIN
Operation
There are three forms of the operation:
1. left outer join, denoted ⟕: takes all tuples in the left relation that did not match with any
tuple in the right relation, pads the tuples with null values for all other attributes from the right
relation, and adds them to the result of the natural join.
2. right outer join, denoted ⟖: is symmetric with the left outer join: It pads tuples from the right
relation that did not match any from the left relation with nulls and adds them to the result of
the natural join.
3. Full outer join ⟗: does both the left and right outer join operations, padding tuples from the
left relation that did not match any from the right relation, as well as tuples from the right
relation that did not match any from the left relation, and adding them to the result of the join.
