Relational Algebra

The Projection operation works on a single relation R and defines a relation that contains a vertical subset of R, extracting the values of specified attributes and eliminating duplicates.

An operation that combines the tuples of two relations, eliminating duplicates to produce a new relation.

The advantage of an Outer Join is that it preserves tuples that would have been lost by other types of joins, ensuring that information is retained.

Relational algebra operations are used to manipulate and query relational databases, allowing for the retrieval, insertion, deletion, and updating of data in a structured manner.

The Cartesian product is a mathematical operation that returns all possible pairs of tuples from two relations, combining each tuple from the first relation with every tuple from the second relation.

Intersection is an operation that returns the set of tuples that are present in both of the input relations.

Set Difference is an operation that returns the elements of one set that are not present in another set.

An example of a Natural Join is listing the names and comments of all clients who have viewed a property for rent.

The union of two relations R and S, which have I and J tuples respectively, is obtained by concatenating them into one relation with a maximum of (I + J) tuples.

The Cartesian product is an operation that returns a set of all possible ordered pairs from two sets, where each pair consists of one element from each set.

UNION is an operation that combines the results of two or more queries, returning all unique records from both sets.

The Selection operation is used to filter tuples from a relation based on specified criteria, such as extracting tuples where Client.clientNo equals Viewing.clientNo.

Both the operands and the results are relations, meaning the output from one operation can become the input to another operation.

SELECTION (or RESTRICTION) is an operation that allows for the retrieval of rows from a relation that satisfy a specified predicate, which can be complex and involve logical operators such as AND, OR, and NOT.

A Semijoin is a relational operation that combines two relations but only returns the attributes of one relation, based on the matching tuples from the other relation.

PROJECTION is an operation that produces a subset of columns from a relation, allowing you to select specific attributes to display, such as staffNo, fName, lName, and salary details.

The logical operators that can be used in SELECTION predicates include ∧ (AND), ∨ (OR), and ~ (NOT).

Intersection is an operation that retrieves the common tuples from two relations, effectively listing all items that exist in both sets.

An example of using Intersection is to list all cities where there is both a branch office and at least one property for rent.

A Full Outer Join is a type of Outer Join that keeps all tuples in both relations, padding tuples with nulls when no matching tuples are found.

Join is a derivative of the Cartesian product, equivalent to performing a Selection operation using the join predicate as the selection formula over the Cartesian product of the two operand relations.

The Selection operation works on a single relation R and defines a relation that contains only those tuples of R that satisfy the specified condition (predicate).

A Natural Join is a type of join operation that automatically removes duplicate occurrences of join attributes from the resulting relation.

An Outer Join is a type of join operation in relational databases that returns all records from one table and the matched records from another table. If there is no match, the result is NULL on the side of the table that does not have a match.

The purpose is to create a relation that includes properties that have been viewed along with comments, as well as those that have not been viewed, ensuring that all properties are represented in the report.

A unary operation that retrieves specific columns from a relation, effectively reducing the number of attributes.

An operation that returns the tuples that are in one relation but not in another, effectively subtracting one set from another.

The Semijoin operation performs a join of the two relations and then projects over the attributes of the first operand.

A Theta join is a type of join that combines rows from two tables based on a condition that is specified using a comparison operator.

The example illustrates the use of Set Difference to identify cities that have a branch office but lack properties available for rent.

Codd (1972 a) originally proposed eight operations in relational algebra, but several others have been developed.

Equijoin is a particular type of Theta join that combines rows from two or more tables based on a related column that has equal values.

An example of using the Cartesian product is to list the names and comments of all clients who have viewed a property for rent by combining two tables, although this may result in unwanted records in the result.

The Natural join operation performs an Equijoin over all the attributes in the two relations that have the same name.

A Left Outer Join is a type of Outer Join that keeps every tuple in the left-hand relation in the result, regardless of whether there is a matching tuple in the right-hand relation.

A Join operation is used to combine rows from two or more tables based on a related column between them, typically used instead of the Cartesian product to satisfy certain conditions.

The Semijoin operation is actually a Semi-Theta join.

An Equijoin is a specific type of Theta join that combines rows from two tables where the join condition is based on equality between specified columns.

An Outer Join is a type of join that returns all rows from one table and the matched rows from the other table, filling in with NULLs where there is no match.

SET DIFFERENCE is an operation that returns the tuples that are present in one relation but not in another.

A Natural Join is a type of join operation in relational databases that automatically joins tables based on columns with the same name and compatible data types.

An example of a SELECTION operation is listing all staff with a salary greater than £10,000.

A Theta Join is a type of join operation in relational databases that combines rows from two or more tables based on a specified condition that uses a comparison operator (such as <, >, =, etc.) to match rows.

The degree of a Natural join is the sum of the degrees of the relations R and S less the number of attributes in x.

A unary operation that selects a subset of tuples from a relation based on a specified condition.

An operation that combines two relations to produce a new relation containing all possible combinations of tuples from both relations.

The variants of the Semijoin operation include Semi-Equijoin and Semi-Natural join.

A Natural join automatically combines rows from two tables based on all columns with the same name and type, eliminating duplicate columns in the result.

Relational algebra operations are used to manipulate and retrieve data from relational databases. They provide a formal foundation for querying and transforming data, allowing for operations such as selection, projection, union, intersection, and joins.

SET operations are used to combine information from several relations, allowing for the union, intersection, and difference of tuples from different relations.

The Cartesian product is an operation that combines two tables by pairing each row from the first table with every row from the second table, resulting in a new table that contains all possible combinations of rows.

The example illustrates the use of a Semijoin to produce a relation consisting of properties that have been viewed with comments and those that have not been viewed.

An Outer Join is a type of join that allows tuples from one relation to appear in the result even when there are no matching values in the other relation, preserving information that would be lost in other types of joins.

A Right Outer Join is a type of Outer Join that keeps every tuple in the right-hand relation in the result, regardless of whether there is a matching tuple in the left-hand relation.

A Semi Join is a type of join that returns rows from one table where there is a match in another table, but does not return columns from the second table.

The relational algebra is a theoretical language with operations that work on one or more relations to define another relation without changing the original relation(s).