Questions and Answers
What is Relational algebra?
A set of mathematical principles that form the basis for manipulating relational table contents; the eight main functions are SELECT, PROJECT, JOIN, INTERSECT, UNION, DIFFERENCE, PRODUCT, and DIVIDE.
The degree of relational completeness can be defined by what?
The extent to which relational algebra is supported.
To be considered minimally relational, the DBMS must do what?
Support the key relational operators SELECT, PROJECT, and JOIN.
What is the difference between 'relation' and 'relvar'?
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What does 'relvar' stand for?
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A relvar has two parts. What are they?
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An unspecified relation is often assigned __________ and relvar is assigned __________.
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What is the property of closure?
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What does SELECT (RESTRICT) yield?
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What does PROJECT yield?
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PROJECT is denoted by?
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What is UNION in relational algebra?
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What does union-compatible mean?
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UNION is denoted by?
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What is INTERSECT in relational algebra?
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INTERSECT is denoted by?
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What is DIFFERENCE in relational algebra?
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What is PRODUCT in relational algebra?
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What is the symbol for PRODUCT?
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What is JOIN in relational algebra?
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What is a Natural Join?
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Explain the 3-step process of Natural Join (JOIN).
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In the 3-step process of Natural Join, what are the common columns created in step 2 referred to as?
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What are join columns?
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JOIN is denoted by?
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In JOIN, if no match is made between the table rows, then the new table includes the unmatched row.
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The column on which the join was made occurs how many times in the new table?
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Study Notes
Relational Algebra Overview
- Relational algebra provides mathematical principles for manipulating relational table contents.
- Eight main functions include: SELECT, PROJECT, JOIN, INTERSECT, UNION, DIFFERENCE, PRODUCT, and DIVIDE.
Relational Completeness
- Defined by the extent to which relational algebra is supported by a Database Management System (DBMS).
- Minimally relational DBMS must support key operators: SELECT, PROJECT, and JOIN.
Concepts of Relation and Relvar
- A relation is the actual data seen in tables, while a relvar is a variable that holds the relation.
- Relvar contains two parts: heading (names of attributes) and body (actual relation data).
Naming Conventions
- An unspecified relation is typically assigned a lower-case letter (e.g., "r"), while a relvar is assigned an upper-case letter (e.g., "R").
Closure Property
- Closure allows relational algebra operators to be applied to existing relations, yielding new relations.
Core Operators in Relational Algebra
- SELECT (RESTRICT): Used to choose a subset of rows from a table; produces a horizontal subset without limiting attributes.
- PROJECT: Selects a subset of columns; produces a vertical subset containing all values for selected attributes, denoted by the Greek letter pi (π).
Set Operations
- UNION: Merges two tables into one while eliminating duplicate rows. Tables must be union-compatible, meaning they have the same number of columns with compatible domains; denoted by symbol ∪.
- INTERSECT: Yields only the rows common to two union-compatible tables; denoted by symbol ∩.
- DIFFERENCE: Produces rows from one table that aren’t found in another, requiring union compatibility.
Cartesian Product
- PRODUCT: Yields all possible pairs of rows from two tables, also known as the Cartesian product, denoted by multiplication symbol (×).
Joins in Relational Algebra
- JOIN: Combines rows from two tables based on defined criteria. Types include natural join, theta join, equijoin, and outer join; denoted by symbol ⨝.
- Natural Join: Results in a new table with rows having common values in shared attributes.
Steps in Natural Join Process
- Step 1: Create the PRODUCT of the tables.
- Step 2: Perform SELECT to keep rows with equal attribute values from Step 1.
- Step 3: Perform PROJECT to provide a single copy of each attribute, eliminating duplicate columns.
Join Columns and Output Characteristics
- Common columns from Step 2 are referred to as join columns.
- JOIN results include join columns only once. If no match occurs between rows, unmatched rows are excluded from the result.
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Description
Test your knowledge of relational algebra and its set operators with these flashcards. Understand the core principles and functions such as SELECT, PROJECT, and JOIN. This quiz will help reinforce your understanding of relational database concepts.