Questions and Answers
Who originally proposed relational algebra in 1972?
Which of the following are five fundamental operations in relational algebra?
What are three other common operations in relational algebra?
Selection is a ___ operation.
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In algebraic terms, a selection operation is expressed by the following notation:
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The symbol 'σ' represents what in relational algebra?
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The symbol 'c' in the selection notation σc(R) represents:
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In algebraic terms, R represents what in the selection operation σc(R)?
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Convert the SQL statement to a selection operation: SELECT * FROM Employee WHERE title = 's_rep';
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What operation is unary and selects columns from a relation?
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In algebraic terms, a projection operation is expressed using the following notation:
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The symbol 'π' in relational algebra corresponds to which operation?
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Convert the following SQL statement to a projection operation: SELECT last_name, title, loc_num FROM Employee;
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Convert the SQL statement to a nested selection operation within the projection operation: SELECT last_name, title, loc_num FROM Employee WHERE title = 's_rep';
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A ___ operation multiplies two relations to create a new relation containing every possible pair of rows from the two original relations.
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What is the algebraic notation for the Cartesian product operation?
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In algebraic terms, a ____ operation is expressed using the following notation R X S.
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Convert the SQL statement to a Cartesian product operation: SELECT Employee., Customer. FROM Employee, Customer;
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A __ is a binary operation that combines all rows into a single relation while eliminating any duplicates.
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For the two relations to be involved in a union, they must be ___.
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In algebra, a ___ operation is expressed using the following notation R ∪ S.
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Union compatibility can be ensured using which operation?
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A __ is a binary operation that creates a relation including the rows that are in the first relation, but not in the second.
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What notation is used for a difference operation?
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How is a difference operation against two employee relations written in SQL?
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An __ is a binary operation that creates a new relation containing all the rows that are in both the first and the second relations.
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What is the algebraic notation for an intersection operation?
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A __ (notated as θjoin) combines two relations where the combination satisfies a predicate.
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What is the algebraic notation for a thetajoin?
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When a thetajoin predicate contains only the equality operator, it’s known as an:
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A ___ is a binary operation that combines two relations over their common attributes.
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Outer join operations allow for rows to appear in the resulting relation even when there are no matching values in the second relation. What notation expresses this?
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Study Notes
Relational Algebra Overview
 Relational algebra was proposed by Dr. E.F. Codd in 1972 and is fundamental for relational databases.
 It provides a theoretical framework for data manipulation languages (DML) and data query languages (DQL).
Fundamental Operations
 Five primary operations define relational algebra:
 Selection
 Projection
 Cartesian product
 Union
 Difference
 Additional common operations include:
 Intersection
 Join
 Division
Selection Operation
 The selection operation is unary, selecting rows based on specified conditions.
 Notated as σc(R), where "σ" indicates selection, "c" is the selection condition, and "R" is the relation.
Projection Operation
 Projection is also unary and selects specific columns from a relation.
 Notated as πA1, A2, A3...An(R), where "π" represents projection and "A1, A2, A3...An" lists the columns to project.
Cartesian Product
 A binary operation that combines every possible pair of rows from two relations, notated as R X S.
 Generates a new relation consisting of all combinations.
Union Operation
 Combines all rows from two relations into a single relation, eliminating duplicates.
 Relations must be unioncompatible, having the same number of matching attributes.
Difference Operation
 The difference operation (R  S) returns rows present in the first relation but not in the second.
 Unioncompatibility is also required here.
Intersection Operation
 Intersection relates to common rows from two relations, noted as R ∩ S.
 Relations must be unioncompatible to apply this operation.
Join Operations
 Join operations combine two relations based on common attributes:
 ThetaJoin: Combines based on specific predicates and is symbolized as R ⨝F S.
 Natural Join: A type of thetajoin that implicitly removes duplicates in common attributes, notated as R ⨝ S.
 Outer Join: Allows rows to appear even without matching values in the joined relation, denoted as R ⟕ S (left outer join) or R ⟖ S (right outer join).
Notation Essentials
 Understanding the symbols:
 σ: Selection operation
 π: Projection operation
 X: Cartesian product
 ∪: Union operation
 : Difference operation
 ∩: Intersection operation
 ⨝: Join operation
 ⟕, ⟖: Outer join operations
SQL Conversion Examples
 Selection from SQL translates to σ:

SELECT * FROM Employee WHERE title = 's_rep'
becomesσtitle='s_rep'(Employee)
.

 Projection from SQL translates to π:

SELECT last_name, title, loc_num FROM Employee
becomesπlast_name, title, loc_num(Employee)
.

 Cartesian product from SQL translates to:

SELECT Employee.*, Customer.* FROM Employee, Customer
becomesEmployee X Customer
.

Application of Operations
 Each operation performs specific data retrieval tasks essential for database management systems, allowing complex queries and data manipulation.
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Description
Test your understanding of relational algebra with these flashcards. This chapter focuses on the key concepts and contributors to the field of relational databases, including important figures like Dr. E.F. Codd. Dive into the theoretical aspects that underpin data manipulation languages.