Relational algebra is a mathematical system for manipulating data stored in a relational database. It consists of a set of fundamental operations, including select, project, set, and rename. Here's an explanation of each operation:

Select: The select operation is used to retrieve a subset of tuples from a relation that satisfy a given condition. This operation is similar to the WHERE clause in SQL. The select operation takes a relation as input and returns a new relation that contains only the tuples that satisfy the given condition.

Project: The project operation is used to retrieve a subset of columns from a relation. This operation is similar to the SELECT clause in SQL, but it returns only the specified columns and removes any duplicate tuples. The project operation takes a relation as input and returns a new relation that contains only the specified columns.

Set: The set operation is used to combine two relations into a single relation. There are three types of set operations: union, intersection, and difference. The union operation combines two relations and removes any duplicate tuples. The intersection operation returns only the tuples that are common to both relations. The difference operation returns the tuples that are in one relation but not the other.

Rename: The rename operation is used to change the name of a relation or a column in a relation. This operation is similar to the AS keyword in SQL. The rename operation takes a relation as input and returns a new relation with the specified name or column name changed.

In summary, the select operation is used to retrieve a subset of tuples that satisfy a given condition, the project operation is used to retrieve a subset of columns, the set operation is used to combine two relations into a single relation, and the rename operation is used to change the name of a relation or a column in a relation. These operations are the fundamental building blocks of relational algebra and are used to manipulate and query data in a relational database.