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# Database Systems Chapter 9

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@BeneficentHonor6192

### Who originally proposed relational algebra in 1972?

• Oracle Corporation
• University of California at Berkeley
• Dr. Peter P. Chen
• Dr. E.F. Codd (correct)
• Dr. Peterlee
• ### Which of the following are five fundamental operations in relational algebra?

• Selection, Forecast, Cartesian product, Union, Difference
• Selection, Projection, Cartesian product, Union, Difference (correct)
• Choice, Projection, Cartesian product, Union, Difference
• Selection, Projection, Cartesian product, Alliance, Difference
• ### What are three other common operations in relational algebra?

• Distribution
• Join (correct)
• Junction
• Division (correct)
• Intersection (correct)
• ### Selection is a ___ operation.

<p>unary</p> Signup and view all the answers

### In algebraic terms, a selection operation is expressed by the following notation:

<p>σc(R)</p> Signup and view all the answers

### The symbol 'σ' represents what in relational algebra?

<p>Represents the selection operation</p> Signup and view all the answers

### The symbol 'c' in the selection notation σc(R) represents:

<p>The condition to use when selecting rows</p> Signup and view all the answers

### In algebraic terms, R represents what in the selection operation σc(R)?

<p>The relation being operated on</p> Signup and view all the answers

### Convert the SQL statement to a selection operation: SELECT * FROM Employee WHERE title = 's_rep';

<p>σtitle = 's_rep'(Employee)</p> Signup and view all the answers

### What operation is unary and selects columns from a relation?

<p>Projection</p> Signup and view all the answers

### In algebraic terms, a projection operation is expressed using the following notation:

<p>πA1, A2, A3...An(R)</p> Signup and view all the answers

### The symbol 'π' in relational algebra corresponds to which operation?

<p>A list of attributes (column names) to project</p> Signup and view all the answers

### Convert the following SQL statement to a projection operation: SELECT last_name, title, loc_num FROM Employee;

<p>πlast_name, title, loc_num(Employee)</p> Signup and view all the answers

### 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';

<p>πlast_name, title, loc_num(σtitle='s_rep'(Employee))</p> Signup and view all the answers

### A ___ operation multiplies two relations to create a new relation containing every possible pair of rows from the two original relations.

<p>Cartesian product</p> Signup and view all the answers

### What is the algebraic notation for the Cartesian product operation?

<p>R X S</p> Signup and view all the answers

### In algebraic terms, a ____ operation is expressed using the following notation R X S.

<p>The Cartesian product operation</p> Signup and view all the answers

### Convert the SQL statement to a Cartesian product operation: SELECT Employee., Customer. FROM Employee, Customer;

<p>Employee X Customer</p> Signup and view all the answers

### A __ is a binary operation that combines all rows into a single relation while eliminating any duplicates.

<p>Union</p> Signup and view all the answers

### For the two relations to be involved in a union, they must be ___.

<p>Union-compatible</p> Signup and view all the answers

### In algebra, a ___ operation is expressed using the following notation R ∪ S.

<p>The union operation</p> Signup and view all the answers

### Union compatibility can be ensured using which operation?

<p>Projection</p> Signup and view all the answers

### A __ is a binary operation that creates a relation including the rows that are in the first relation, but not in the second.

<p>Difference</p> Signup and view all the answers

### What notation is used for a difference operation?

<p>R - S</p> Signup and view all the answers

### How is a difference operation against two employee relations written in SQL?

<p>SELECT * FROM Employee1 EXCEPT (SELECT e2_id FROM Employee2);</p> Signup and view all the answers

### An __ is a binary operation that creates a new relation containing all the rows that are in both the first and the second relations.

<p>Intersection</p> Signup and view all the answers

### What is the algebraic notation for an intersection operation?

<p>R ∩ S</p> Signup and view all the answers

### A __ (notated as θ-join) combines two relations where the combination satisfies a predicate.

<p>Theta-join</p> Signup and view all the answers

### What is the algebraic notation for a theta-join?

<p>R ⨝F S</p> Signup and view all the answers

### When a theta-join predicate contains only the equality operator, it’s known as an:

<p>Equi-join</p> Signup and view all the answers

### A ___ is a binary operation that combines two relations over their common attributes.

<p>Natural join</p> Signup and view all the answers

### 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?

<p>R ⟕ S or R ⟖ S</p> Signup and view all the answers

## 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
• 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 union-compatible, 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.
• Union-compatibility is also required here.

### Intersection Operation

• Intersection relates to common rows from two relations, noted as R ∩ S.
• Relations must be union-compatible to apply this operation.

### Join Operations

• Join operations combine two relations based on common attributes:
• Theta-Join: Combines based on specific predicates and is symbolized as R ⨝F S.
• Natural Join: A type of theta-join 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' becomes σtitle='s_rep'(Employee).
• Projection from SQL translates to π:
• SELECT last_name, title, loc_num FROM Employee becomes πlast_name, title, loc_num(Employee).
• Cartesian product from SQL translates to:
• SELECT Employee.*, Customer.* FROM Employee, Customer becomes Employee 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.

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