Q.a) Display all possible combinations of tuples of relations DANCE and MUSIC.

Relational Algebra Operations: A First Look

Think of a relational database as a collection of neat, rectangular tables. Each table has rows (records) and columns (attributes). Now, suppose you want to ask questions of this data — "Which customers live in Delhi?" or "Show me all orders placed last month." Relational algebra is the set of basic operations you use to answer such questions. It is the language of queries at the most fundamental level.

You do not need to write code or do math. You only need to understand what each operation does to a table — like a set of tools in a toolbox.

The Core Operations

There are eight classic operations. They fall into two groups: those that work on one table at a time, and those that combine two tables.

Operations on a Single Table

Select (also called Restrict) — This operation picks certain rows from a table based on a condition. For example, from a table of students, you might select only those rows where the city is "Mumbai". The result is a smaller table with the same columns but fewer rows.

Project — This operation picks certain columns from a table. For example, from a student table with columns Roll No, Name, City, and Marks, you might project only Name and City. The result is a table with fewer columns. Duplicate rows are automatically removed.

Rename — This operation simply gives a new name to the resulting table or to its columns. It is useful when you need to refer to the same table more than once in a query, or when you want clearer column headings.

Operations That Combine Two Tables

Union — This combines two tables that have the same structure (same number of columns and compatible data types). The result contains all rows that appear in either table, with duplicates removed. Think of it as "add the rows of one table to the rows of another, but keep only unique ones."

Set Difference — This gives you rows that are in the first table but not in the second. For example, "Which students are enrolled in Course A but not in Course B?"

Intersection — This gives you rows that appear in both tables. For example, "Which customers have bought both a laptop and a printer?"

Cartesian Product — This pairs every row of the first table with every row of the second table. If the first table has 10 rows and the second has 5, the result has 50 rows. This operation is rarely used alone — it is the foundation for the most powerful operation of all.

Join — This is the heart of relational algebra. A join combines rows from two tables based on a related column between them. For example, you have a Customers table and an Orders table. The join operation matches each order to the customer who placed it, using the Customer ID column that appears in both tables. The result is a single table with all the customer details alongside their orders.

Why Relational Algebra Matters …