What is the purpose of relational algebra in database management systems?a.To manipulate and query data stored in relational databasesb.To optimize database performancec.To define database schemasd.To design user interfaces for databases

The purpose of relational algebra in database management systems is to manipulate and query data stored in relational databases. It provides a framework for describing data with relational model, expressing queries on it and performing operations on it.

Here's a step-by-step breakdown:

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

2. The basic operations of relational algebra include select, project, union, set difference, Cartesian product, rename, join, division etc. Each of these operations takes one or two relations as input and produces a new relation as a result.

3. These operations allow us to manipulate the data, extract the required information from the database, and present it in different ways as per the requirements.

4. For example, the 'select' operation allows us to choose a subset of tuples in a relation that satisfy a selection condition. The 'project' operation allows us to choose certain columns from the table and discard the others.

5. Relational algebra is also used in optimizing queries for efficiency. The database management system can transform a given query into different equivalent queries, and choose the one that can be executed most efficiently.

So, the correct answer to your question is (a) To manipulate and query data stored in relational databases.