A set of tuples with a defined header. Each tuple has the same attributes, and values in each attribute come from an appropriate domain.

What is the arity of a relation?

The number of attributes in each tuple, corresponding to the number of columns in a table.

What does union compatibility mean?

The relations have the same set of attributes, with corresponding attributes compatible so their tuples can be compared and combined.

What is a Cartesian product?

A binary operation that combines every tuple in one relation with every tuple in another, producing flattened tuples with attributes from both.

What is the cardinality of a Cartesian product?

The product of the input cardinalities: $|R \times S|=|R|\times|S|$.

DatabasesLesson 3 of 5 in the course Relational model and SQL

Relational Algebra: Core Operators, Query Optimization, and SQL Semantics

5 flashcards · 5 quiz questions · 5 match pairs · 5 fill-in sentences · English

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Summary

Relational algebra provides a precise way to describe transformations of tabular data. It is a theoretical foundation for relational databases and helps explain how database queries can be combined and optimized.

A relation of arity $n$ is a set of $n$ -tuples. In a table, each tuple corresponds to a row, and each position in a tuple corresponds to an attribute or column. The arity is the number of attributes; the number of tuples is the number of rows.

All flashcards

What is a relation?: A set of tuples with a defined header. Each tuple has the same attributes, and values in each attribute come from an appropriate domain.
What is the arity of a relation?: The number of attributes in each tuple, corresponding to the number of columns in a table.
What does union compatibility mean?: The relations have the same set of attributes, with corresponding attributes compatible so their tuples can be compared and combined.
What is a Cartesian product?: A binary operation that combines every tuple in one relation with every tuple in another, producing flattened tuples with attributes from both.
What is the cardinality of a Cartesian product?: The product of the input cardinalities: $|R \times S|=|R|\times|S|$ .

Quiz questions

In classical relational algebra, what happens to duplicate tuples produced by projection?Answer: They are eliminated because the result is a set.
What does a left outer join preserve when no matching tuple exists on the right?Answer: The unmatched left tuple, with null-like values for right-side attributes.
What does transitive closure of a binary relation represent?Answer: Pairs connected by a path of one or more links.
Why might a query optimizer push a selection closer to an input relation?Answer: Filtering earlier can reduce the size of intermediate results.
How do SQL query results commonly treat duplicate rows by default?Answer: They may retain duplicates, following bag rather than set semantics.

Based on the Wikipedia article Relational algebra, licensed CC BY-SA 4.0. Adapted into a summary, flashcards and quizzes.

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