Questions and Answers
What is relational algebra?
What are the five fundamental operations in relational algebra?
Selection, Projection, Cartesian product, Union, Set difference
What are the two unary operations in relational algebra?
Selection and Projection
What does the Selection operation do in relational algebra?
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What is the purpose of the Projection operation?
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What does the Union operation do?
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What is the Set difference operation?
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What does the Intersection operation return?
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What is the Cartesian product in relational algebra?
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Which of the following is NOT a type of join operation?
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What defines a Theta join?
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What is the Equijoin operation?
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What does a Natural join do?
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What is a Left Outer join?
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What does Semijoin return?
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What does the Division operation do?
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What is the COUNT aggregate function used for?
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Study Notes
Relational Algebra
- A theoretical language used for modeling data in relational databases.
- Consists of operations that manipulate relations without altering the original data.
- Introduced by Edgar F. Codd while at IBM, forming the foundation for query languages like SQL.
Fundamental Operations
- Selection (Restriction): Filters tuples based on a specified condition.
- Projection: Extracts specific attributes from a relation while eliminating duplicates.
- Cartesian Product: Combines every tuple from two relations.
- Union: Merges two relations, including all unique tuples from both.
- Set Difference: Returns tuples from one relation that are not in another.
- Additional operations include Join, Intersection, and Division, expressible through fundamental operations.
Unary Operations
- Selection and Projection: Operate on a single relation to extract information.
Selection
- Notated as σpredicate(R), it yields tuples from relation R that meet a condition.
- SQL equivalent uses WHERE clause in select statements, handling three possible truth values (true, false, unknown).
Projection
- Notated as Πa1..., an(R), it generates a subset of R's columns while removing duplicates.
Union
- Notated as R ∪ S; combines tuples from relations R and S, ensuring they are union-compatible.
Set Difference
- Notated as R - S; defines tuples in R that are absent in S, requiring union compatibility.
Intersection
- Notated as R ∩ S; identifies tuples common to both R and S, with union compatibility required.
Cartesian Product
- Notated as R × S; produces a relation formed by pairing each tuple of R with every tuple of S.
Join Operations
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Types include:
- Theta Join
- Equijoin (a specific Theta join)
- Natural join
- Outer join
- Semijoin
Theta Join
- Notated as R ⋈FS; produces tuples from the Cartesian product satisfying a specified predicate.
EquiJoin
- A specific case of Theta Join where the predicate involves only equality.
Natural Join
- Notated as R ⋈ S; merges relations R and S on all common attributes, resulting in a single occurrence of shared attributes.
Outer Join
- Notated as R ⋊ S; includes tuples from R that lack matches in S, filling gaps with null values.
Semijoin
- Notated as R ▹F S; returns tuples from R based on participation in the join satisfying a condition.
Division
- Notated as R ÷ S; forms a relation over attributes C that corresponds to all tuple combinations matching those in S.
Aggregate Functions
- COUNT: Counts the number of values in an attribute.
- SUM: Returns the total of numeric attributes (details not provided).
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Description
This quiz explores the fundamental concepts of relational algebra, a theoretical framework used in relational databases. It covers key operations like selection, projection, and union, as well as the significance of these concepts in query languages such as SQL.
