Q.(a) Consider the following tables - LOAN and BORROWER: Table: LOAN LOAN_NO B_NAME AMOUNT L-170 DELHI 3000 L-230 KANPUR 4000 Table: BORROWER CUST_NAME LOAN_NO JOHN L-171 KRISH L-230 RAVYA L-170 How many rows and columns will be there in the natural join of these two tables?

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 …

Database Querying: Asking Questions of a Data Collection

Think of a library. You walk in, and instead of wandering through endless shelves, you go to the librarian and say: "I need all books by R. K. Narayan published after 1980." The librarian knows exactly where to look, finds the relevant books, and hands you a short list. That act of asking — of specifying exactly what you want from a large, organised collection — is the essence of querying.

A database is like that library, but for digital information. It stores data in a structured way, typically in tables with rows and columns. A query is simply a question you ask of that database. You don't need to know where the data lives or how it's stored internally. You just need to state what you want.

The Precise Meaning

In formal terms, a database query is a request for data or information from a database. The request is written in a special language that the database understands. The most common such language is SQL (Structured Query Language), but the concept of querying exists in every database system.

When you query a database, you are doing one of four things:

• Retrieving data (the most common — "show me the customers who live in Delhi")
• Inserting new data ("add this new student record")
• Updating existing data ("change this address")
• Deleting data ("remove this old order")

For a commerce or humanities student, the retrieval part is where the real power lies. You are not just pulling out raw data — you are filtering, sorting, and combining it to get answers.

Why It Matters

A database without querying is like a library with the lights off. The data exists, but you cannot use it. Querying turns stored facts into actionable information.

Consider a small business owner who keeps customer records in a spreadsheet. Without querying, they might scroll through hundreds of rows to find customers who haven't purchased in six months. With a query, they type one request and get the answer instantly. That answer might lead to a targeted marketing campaign, which brings in revenue.

The Intuition Behind It

Every query has a simple structure at its core:

1. What data do you want? (Which columns or fields?)
2. Where is it? (Which table or collection?)
3. Under what conditions? (Which rows match your criteria?)

If you can answer those three questions in plain English, you are already thinking like someone who queries databases. The technical language (SQL) is just a way to write those answers down so the computer understands.

A Real-World Example …