DBMS Update Qb Solution PDF

Sure! Here are the answers to the short and long questions: ### Short Questions 1. **Define: Data, Database, DBMS, Data Redundancy** - **Data**: Raw facts or figures that can be processed to extract meaningful information. Example: Numbers, dates, names. - **Database**: An organized collectio...

Sure! Here are the answers to the short and long questions: ### Short Questions 1. **Define: Data, Database, DBMS, Data Redundancy** - **Data**: Raw facts or figures that can be processed to extract meaningful information. Example: Numbers, dates, names. - **Database**: An organized collection of related data stored and accessed electronically. Example: A customer database with tables for customer information, orders, and payments. - **DBMS (Database Management System)**: Software that manages databases and allows for the creation, manipulation, and querying of data. Example: MySQL, Oracle. - **Data Redundancy**: The duplication of data within a database or across different databases. Example: Storing the same customer address in multiple tables. 2. **What is data and information?** - **Data**: Raw, unprocessed facts and figures. Example: A list of numbers or names. - **Information**: Data that has been processed and organized to have meaning and relevance. Example: A summary report showing sales trends over the past year. 3. **Give the difference between data and information.** - **Data**: Unprocessed, raw input. Example: "John", "100", "2024".  - **Information**: Processed data that provides context and meaning. Example: "John earned $100 in 2024." 4. **Why do we need a DBMS?** - **Efficient Data Management**: Facilitates the storage, retrieval, and manipulation of data. - **Data Integrity and Accuracy**: Enforces rules to ensure data consistency and correctness. - **Data Security**: Provides mechanisms for controlling access to data. - **Backup and Recovery**: Offers tools for backing up data and recovering it in case of loss. 5. **Give the application of DBMS.** - **Online Transaction Processing (OLTP)**: Used in applications like banking systems for transaction management. - **Customer Relationship Management (CRM)**: Manages customer interactions and data. - **Enterprise Resource Planning (ERP)**: Integrates various business processes and data. - **E-commerce**: Manages product listings, orders, and customer data for online shopping. 6. **Explain the advantages and disadvantages of DBMS.** - **Advantages**: - **Centralized Data Management**: Simplifies data management by centralizing data.  - **Improved Data Integrity**: Ensures accuracy and consistency with constraints and validation rules. - **Enhanced Security**: Provides access controls to protect data. - **Data Redundancy Reduction**: Minimizes duplication through normalization. - **Disadvantages**: - **Cost**: Can be expensive to purchase and maintain. - **Complexity**: Requires specialized knowledge to manage and configure. - **Performance Overhead**: May introduce latency compared to simpler file systems. - **Maintenance**: Requires regular updates and monitoring. 7. **What is schema and instance? Explain with example.** - **Schema**: The overall design and structure of the database, including tables, relationships, and constraints. Example: A university database schema might include tables for students, courses, and enrollments, with specific relationships and constraints defined. - **Instance**: A snapshot of the database at a particular moment in time, representing the actual data stored. Example: The list of students currently enrolled in courses at the start of a semester. ### Long Questions 8. **Give the difference between FPS and DBMS.** - **FPS (File Processing System)**:  - **Data Storage**: Data is stored in individual files with no inherent relationships. - **Querying**: Limited querying capabilities; often requires custom coding. - **Data Redundancy**: High; data can be duplicated across files. - **Flexibility**: Changes to data structure require modifications to application code. - **DBMS**: - **Data Storage**: Data is stored in structured tables with defined relationships. - **Querying**: Supports complex queries using SQL. - **Data Redundancy**: Reduced through normalization and central management. - **Flexibility**: Changes to the data structure can be managed more easily with minimal impact on applications. 9. **Why DBMS is Better than FPS?** - **Data Integrity and Consistency**: DBMS enforces rules and constraints to ensure data accuracy, reducing redundancy and anomalies. - **Efficient Data Retrieval**: Supports sophisticated querying and indexing for faster data access. - **Security**: Provides user access controls and permissions to protect data. - **Backup and Recovery**: Offers automated backup and recovery solutions to prevent data loss. 10. **Explain in detail the three-layer architecture or ANSI/SPARC model of DBMS.**  - **External Level**: Also known as the user view level, this layer defines how users view the data. It includes different user views and can have multiple user-specific views. Example: A sales manager might have a view focusing on sales data, while an HR manager might see employee-related data. - **Conceptual Level**: The logical level that defines the database structure as a whole. It includes the schema of the database, describing entities, relationships, and constraints. Example: The schema defining tables for employees, departments, and their relationships. - **Internal Level**: The physical level that details how data is stored on the storage medium. It includes storage structures, indexes, and file organization. Example: Data stored on disk files, organized into blocks. 11. **What is Client-server architecture/Database architecture? Explain 1-tier, 2-tier, 3-tier architecture with diagrams.** - **1-Tier Architecture**: Also known as a standalone or single-tier architecture, where the application and database reside on the same machine. - **Diagram**: ``` [Application + Database] ``` - **2-Tier Architecture**: Consists of a client and a server. The client directly interacts with the database server. - **Diagram**: ``` [Client] → [Database Server] ``` - **3-Tier Architecture**: Includes three layers:  - **Presentation Layer**: The client or user interface. - **Application Layer**: The middle tier or application server. - **Database Layer**: The back-end database server. - **Diagram**: ``` [Client (Presentation Layer)] ↓ [Application Server (Application Layer)] ↓ [Database Server (Database Layer)] ``` 12. **Explain the types of users of DBA.** - **Database Administrator (DBA)**: Responsible for the overall management, maintenance, and security of the database system. - **Database Designer**: Focuses on designing the database schema, including tables, relationships, and constraints. - **Database Developer**: Develops applications and scripts to interact with the database, including data manipulation and retrieval. - **Database Analyst**: Analyzes data and provides insights for decision- making, often generating reports and performing data mining. 13. **What is data independence? Explain the difference between physical and logical data independence with examples.** - **Data Independence**: The ability to change the database schema without affecting the application programs.  - **Physical Data Independence**: Changes to the physical storage of data do not affect the logical schema. Example: Moving data from one storage device to another does not require changes to the database design or applications that use the database. - **Logical Data Independence**: Changes to the logical schema (structure) do not affect application programs. Example: Adding a new column to a table does not require changes to the application programs that use the table, provided that the new column does not impact existing queries. Sure! Here are the detailed answers to the SQL-related questions: ### Short Questions 12. **Explain the significance of logical operators (AND/OR) in SQL predicates. Provide an example illustrating their use.** - **Logical Operators**: Used to combine multiple conditions in SQL queries to refine data retrieval. - **AND**: Combines conditions where all must be true. Example: `SELECT * FROM Employees WHERE Age > 30 AND Salary > 50000;` - **OR**: Combines conditions where at least one must be true. Example: `SELECT * FROM Employees WHERE Age > 30 OR Salary > 50000;` - **NOT**: Negates a condition. Example: `SELECT * FROM Employees WHERE NOT City = 'New York';` - **Significance**: They allow for more complex queries, enabling more precise data retrieval based on multiple criteria. 13. **Discuss the use of the BETWEEN predicate in SQL. Provide an example demonstrating its application.** - **BETWEEN**: Used to filter records within a specific range of values. - **Syntax**: `column_name BETWEEN value1 AND value2` - **Example**: To find products with a price between 50 and 100: ```sql SELECT * FROM Products WHERE Price BETWEEN 50 AND 100; ``` - **Significance**: Simplifies queries that need to filter data within a range, making queries more readable and concise. 14. **Explain in Detail Aggregate function in SQL.** - **Aggregate Functions**: Perform calculations on multiple values and return a single value. - **COUNT()**: Counts the number of rows. Example: `SELECT COUNT(*) FROM Orders;` - **SUM()**: Adds up all values in a numeric column. Example: `SELECT SUM(Amount) FROM Payments;` - **AVG()**: Calculates the average of values in a numeric column. Example: `SELECT AVG(Salary) FROM Employees;` - **MAX()**: Returns the maximum value from a column. Example: `SELECT MAX(Salary) FROM Employees;` - **MIN()**: Returns the minimum value from a column. Example: `SELECT MIN(Salary) FROM Employees;` - **Significance**: Useful for summarizing and analyzing data, providing insights like totals, averages, and extremes. 15. **Write a short note on character functions in SQL.** - **Character Functions**: Manipulate and format string data. - **CONCAT()**: Joins two or more strings. Example: `SELECT CONCAT(FirstName, ' ', LastName) AS FullName FROM Employees;` - **SUBSTRING()**: Extracts a portion of a string. Example: `SELECT SUBSTRING(FirstName, 1, 3) FROM Employees;` - **LENGTH()**: Returns the length of a string. Example: `SELECT LENGTH(FirstName) FROM Employees;` - **UPPER()**: Converts a string to uppercase. Example: `SELECT UPPER(FirstName) FROM Employees;` - **LOWER()**: Converts a string to lowercase. Example: `SELECT LOWER(FirstName) FROM Employees;` - **Significance**: Useful for formatting and manipulating string data to meet specific requirements or for data cleaning. ### Long Questions 16. **What do you mean by SQL? Discuss the different languages of SQL and its commands.** - **SQL (Structured Query Language)**: A standard language used to communicate with and manage relational databases. It allows users to perform various operations on data stored in relational databases. - **Languages of SQL**:  - **DDL (Data Definition Language)**: Used to define and manage database structures. - **Commands**: - **CREATE**: Defines new database objects (e.g., tables, indexes). Example: `CREATE TABLE Employees (ID INT, Name VARCHAR(100));` - **ALTER**: Modifies existing database objects. Example: `ALTER TABLE Employees ADD COLUMN Age INT;` - **DROP**: Deletes database objects. Example: `DROP TABLE Employees;` - **DML (Data Manipulation Language)**: Used to manipulate and retrieve data from tables. - **Commands**: - **SELECT**: Retrieves data from one or more tables. Example: `SELECT * FROM Employees;` - **INSERT**: Adds new rows to a table. Example: `INSERT INTO Employees (ID, Name) VALUES (1, 'John Doe');` - **UPDATE**: Modifies existing rows. Example: `UPDATE Employees SET Age = 30 WHERE ID = 1;` - **DELETE**: Removes rows from a table. Example: `DELETE FROM Employees WHERE ID = 1;` - **DCL (Data Control Language)**: Used to control access to data in the database. - **Commands**: - **GRANT**: Provides users with specific permissions. Example: `GRANT SELECT ON Employees TO user1;` - **REVOKE**: Removes specific permissions from users. Example: `REVOKE SELECT ON Employees FROM user1;`  - **TCL (Transaction Control Language)**: Used to manage transactions in the database. - **Commands**: - **COMMIT**: Saves all changes made during the current transaction. Example: `COMMIT;` - **ROLLBACK**: Undoes changes made during the current transaction. Example: `ROLLBACK;` - **SAVEPOINT**: Sets a point within a transaction to which you can roll back. Example: `SAVEPOINT sp1;` 17. **Explain in detail DDL and its commands.** - **DDL (Data Definition Language)**: Manages database schema and structure. - **Commands**: - **CREATE**: Defines new database objects. - **Table**: Creates a new table. Example: ```sql CREATE TABLE Employees ( ID INT PRIMARY KEY, Name VARCHAR(100), HireDate DATE ); ``` - **Index**: Creates an index on a table to speed up queries. Example: ```sql CREATE INDEX idx_name ON Employees (Name);  ``` - **View**: Creates a virtual table based on a query. Example: ```sql CREATE VIEW EmployeeView AS SELECT Name, HireDate FROM Employees; ``` - **ALTER**: Modifies existing database objects. - **Add Column**: Adds a new column to an existing table. Example: ```sql ALTER TABLE Employees ADD COLUMN Department VARCHAR(50); ``` - **Modify Column**: Changes the data type or size of a column. Example: ```sql ALTER TABLE Employees MODIFY COLUMN Name VARCHAR(150); ``` - **Drop Column**: Removes a column from a table. Example: ```sql ALTER TABLE Employees DROP COLUMN Department; ``` - **DROP**: Deletes existing database objects. - **Table**: Deletes an entire table and its data. Example: ```sql DROP TABLE Employees;  ``` - **Index**: Deletes an index. Example: ```sql DROP INDEX idx_name ON Employees; ``` - **View**: Deletes a view. Example: ```sql DROP VIEW EmployeeView; ``` 18. **Explain in detail DML and its commands.** - **DML (Data Manipulation Language)**: Handles the manipulation of data within tables. - **Commands**: - **SELECT**: Retrieves data from one or more tables. - Example: `SELECT * FROM Employees;` - **SELECT DISTINCT**: Retrieves unique values. Example: `SELECT DISTINCT Department FROM Employees;` - **WHERE**: Filters data based on conditions. Example: `SELECT * FROM Employees WHERE Age > 30;` - **ORDER BY**: Sorts results. Example: `SELECT * FROM Employees ORDER BY HireDate DESC;` - **INSERT**: Adds new rows to a table. - Example:  ```sql INSERT INTO Employees (ID, Name, HireDate) VALUES (1, 'John Doe', '2023-01-15'); ``` - **UPDATE**: Modifies existing rows in a table. - Example: ```sql UPDATE Employees SET Salary = 60000 WHERE ID = 1; ``` - **DELETE**: Removes rows from a table. - Example: ```sql DELETE FROM Employees WHERE ID = 1; ``` 19. **Write a short note on logical operators.** - **Logical Operators**: Used in SQL to combine multiple conditions in WHERE clauses or other logical expressions. - **AND**: Returns true if all conditions are true. Example: `SELECT * FROM Orders WHERE Quantity > 10 AND Price < 100;`  - **OR**: Returns true if at least one condition is true. Example: `SELECT * FROM Orders WHERE Quantity > 10 OR Price < 100;` - **NOT**: Negates a condition. Example: `SELECT * FROM Orders WHERE NOT (Quantity > 10);` - **Significance**: They help in constructing complex queries to filter data based on multiple criteria. 20. **Write a short note on Relational operators.** - **Relational Operators**: Used to compare values in SQL queries. - **=**: Equal to. Example: `SELECT * FROM Employees WHERE Age = 30;` - ** or !=**: Not equal to. Example: `SELECT * FROM Employees WHERE Age 30;` - **>**: Greater than. Example: `SELECT * FROM Employees WHERE Salary > 50000;` - **=**: Greater than or equal to. Example: `SELECT * FROM Employees WHERE Age >= 30;` - **---- [Instructor] | | (M:1) ``` In this ER diagram: - `Student` is related to `Course` through the `Enrolls` relationship (many-to- many). - `Instructor` is related to `Course` through the `Teaches` relationship (one- to-many).  - `Student` is related to `Department` through the `BelongsTo` relationship (many-to-one). - `Department` is related to `Instructor` through the `ManagedBy` relationship (one-to-one). ### Short Questions 34. **Define the NOT NULL constraint and give an example of its use.** - **NOT NULL Constraint**: Ensures that a column cannot have a NULL value. It enforces that a field must contain a value when a record is inserted or updated in the database. - **Example**: ```sql CREATE TABLE Employees ( EmployeeID INT NOT NULL, Name VARCHAR(100) NOT NULL, HireDate DATE NOT NULL, PRIMARY KEY (EmployeeID) ); ``` In this example, the `EmployeeID`, `Name`, and `HireDate` columns must have values for every row. No NULL values are allowed. 35. **How does a check constraint enhance data integrity in databases?**  - **Check Constraint**: Ensures that values in a column satisfy a specific condition or rule. It enforces data validity by restricting the range or format of data that can be entered into a column. - **Enhancement of Data Integrity**: - **Validates Data**: Ensures that only valid data is entered, reducing errors and inconsistencies. - **Maintains Accuracy**: Helps in maintaining the accuracy of data by enforcing rules such as value ranges or specific formats. - **Example**: ```sql CREATE TABLE Employees ( EmployeeID INT PRIMARY KEY, Name VARCHAR(100), Salary DECIMAL(10, 2) CHECK (Salary > 0) ); ``` In this example, the `Salary` column must have a positive value. Any attempt to insert or update the salary with a non-positive value will be rejected. 36. **Describe the selection operation in relational algebra.** - **Selection Operation**: The selection operation (`σ`) in relational algebra is used to filter rows from a relation based on a specified condition. It selects a subset of rows that satisfy the given predicate. - **Notation**: `σ_condition(Relation)`  - **Example**: - Given a relation `Employees(Name, Age, Salary)`: ```sql σ_Age > 30(Employees) ``` This operation selects all employees whose age is greater than 30. 37. **What are aggregate functions in SQL and give examples of their usage?** - **Aggregate Functions**: Functions that perform calculations on a set of values and return a single value. They are used to summarize or aggregate data. - **Examples**: - **COUNT()**: Counts the number of rows. ```sql SELECT COUNT(*) FROM Employees; ``` - **SUM()**: Adds up the values in a numeric column. ```sql SELECT SUM(Salary) FROM Employees; ``` - **AVG()**: Calculates the average value of a numeric column. ```sql SELECT AVG(Salary) FROM Employees; ``` - **MAX()**: Finds the maximum value in a column.  ```sql SELECT MAX(Salary) FROM Employees; ``` - **MIN()**: Finds the minimum value in a column. ```sql SELECT MIN(Salary) FROM Employees; ``` 38. **What is the relational data model and how does it organize data?** - **Relational Data Model**: Organizes data into tables (relations), where each table is a collection of rows (tuples) and columns (attributes). The relational model uses a structured approach to represent data and relationships through primary and foreign keys. - **Organization**: - **Tables**: Data is organized into tables, each representing an entity (e.g., `Employees`, `Departments`). - **Rows**: Each row in a table represents an individual record or instance of the entity. - **Columns**: Columns represent attributes of the entity, with each column having a specific data type. - **Keys**: - **Primary Key**: Uniquely identifies each record in a table. - **Foreign Key**: Links records in one table to records in another table, establishing relationships between tables. 39. **Define the degree of a relation in the context of a relational database.**  - **Degree of a Relation**: The number of attributes (columns) in a relation (table). It indicates the number of fields in a table. - **Example**: - For a relation `Employees(EmployeeID, Name, Age, Salary)`, the degree is 4, because there are four attributes. 40. **Explain cardinality constraints in the context of relational databases.** - **Cardinality Constraints**: Define the number of instances of one entity that can or must be associated with instances of another entity in a relationship. They enforce rules about how entities are related in terms of quantity. - **Types**: - **One-to-One (1:1)**: A single instance of entity A is associated with a single instance of entity B. Example: A person has only one passport. - **One-to-Many (1:N)**: A single instance of entity A can be associated with multiple instances of entity B, but each instance of B is associated with one instance of A. Example: A department can have many employees. - **Many-to-One (N:1)**: Multiple instances of entity A are associated with a single instance of entity B. Example: Many orders can be placed by one customer. - **Many-to-Many (M:N)**: Multiple instances of entity A can be associated with multiple instances of entity B. Example: Students and courses, where students can enroll in many courses and each course can have many students. ### Long Questions 41. **Describe how the JOIN operation works in relational algebra. Provide examples of different types of joins and when each is useful.** - **JOIN Operation**: Combines tuples from two relations based on a related attribute. It is used to retrieve related data from multiple tables. - **Types of Joins**: - **Inner Join**: Combines rows from both tables where the join condition is met. - **Example**: ```sql SELECT * FROM Employees INNER JOIN Departments ON Employees.DepartmentID = Departments.DepartmentID; ``` - **Use Case**: Retrieve employees and their department details where there is a match. - **Left Outer Join (or Left Join)**: Returns all rows from the left table and matched rows from the right table. If no match, NULL values are returned for columns from the right table. - **Example**: ```sql SELECT * FROM Employees LEFT JOIN Departments ON Employees.DepartmentID = Departments.DepartmentID;  ``` - **Use Case**: Retrieve all employees and their department details, including employees who are not assigned to any department. - **Right Outer Join (or Right Join)**: Returns all rows from the right table and matched rows from the left table. If no match, NULL values are returned for columns from the left table. - **Example**: ```sql SELECT * FROM Employees RIGHT JOIN Departments ON Employees.DepartmentID = Departments.DepartmentID; ``` - **Use Case**: Retrieve all departments and employees in those departments, including departments without employees. - **Full Outer Join**: Returns all rows from both tables. When there is no match, NULL values are returned for columns from the table that does not have a match. - **Example**: ```sql SELECT * FROM Employees FULL OUTER JOIN Departments ON Employees.DepartmentID = Departments.DepartmentID; ```  - **Use Case**: Retrieve all employees and departments, including those without matches in the other table. - **Cross Join**: Returns the Cartesian product of the two tables, combining each row from the first table with each row from the second table. - **Example**: ```sql SELECT * FROM Employees CROSS JOIN Departments; ``` - **Use Case**: Generate a combination of all rows from both tables. This can be useful for generating combinations in simulations or reporting. 42. **Discuss the purpose of constraints in database management. Explain all constraints with appropriate examples.** - **Purpose of Constraints**: Constraints enforce rules and data integrity in a database, ensuring that the data stored is accurate, valid, and consistent. - **Types of Constraints**: - **Primary Key Constraint**: Uniquely identifies each record in a table. No two rows can have the same primary key value. - **Example**: ```sql CREATE TABLE Employees ( EmployeeID INT PRIMARY KEY, Name VARCHAR(100)  ); ``` - **Foreign Key Constraint**: Ensures referential integrity by linking a column in one table to the primary key of another table. - **Example**: ```sql CREATE TABLE Orders ( OrderID INT PRIMARY KEY, CustomerID INT, FOREIGN KEY (CustomerID) REFERENCES Customers(CustomerID) ); ``` - **Unique Constraint**: Ensures that all values in a column are unique across the table. - **Example**: ```sql CREATE TABLE Users ( Username VARCHAR(50) UNIQUE, Password VARCHAR(50) ); ``` - **Check Constraint**: Ensures that all values in a column satisfy a specific condition. - **Example**:  ```sql CREATE TABLE Employees ( Salary DECIMAL(10, 2) CHECK (Salary > 0) ); ``` - **Not Null Constraint**: Ensures that a column cannot have NULL values. - **Example**: ```sql CREATE TABLE Employees ( Name VARCHAR(100) NOT NULL ); ``` 43. **Explain the following terms with a suitable example:** - **Primary Key**: A unique identifier for each record in a table. - **Example**: ```sql CREATE TABLE Students ( StudentID INT PRIMARY KEY, Name VARCHAR(100) ); ```  - **Candidate Key**: An attribute or set of attributes that can uniquely identify a record. A table may have multiple candidate keys. - **Example**: ```sql CREATE TABLE Employees ( EmployeeID INT, Email VARCHAR(100), PRIMARY KEY (EmployeeID) ); ``` In this case, both `EmployeeID` and `Email` could be candidate keys if `Email` is unique. - **Foreign Key**: An attribute that creates a link between two tables, referencing the primary key of another table. - **Example**: ```sql CREATE TABLE Orders ( OrderID INT PRIMARY KEY, CustomerID INT, FOREIGN KEY (CustomerID) REFERENCES Customers(CustomerID) ); ``` 44. **Explain selection and projection operations with examples.**  - **Selection Operation**: Retrieves rows from a table that meet a specific condition. - **Notation**: `σ_condition(Relation)` - **Example**: ```sql SELECT * FROM Employees WHERE Salary > 50000; ``` This SQL query selects all employees with a salary greater than 50,000. - **Projection Operation**: Retrieves specific columns from a table, excluding others. - **Notation**: `π_columns(Relation)` - **Example**: ```sql SELECT Name, Salary FROM Employees; ``` This SQL query selects only the `Name` and `Salary` columns from the `Employees` table. 45. **What is database schema? Explain the SELECT, PROJECT, NATURAL JOIN, UNION, and CARTESIAN PRODUCT operations.** - **Database Schema**: The structure that defines the organization of data in a database. It includes tables, columns, relationships, and constraints.  - **Operations**: - **SELECT (σ)**: Retrieves rows that satisfy a specified condition. - **Example**: ```sql SELECT * FROM Employees WHERE Department = 'HR'; ``` - **PROJECT (π)**: Retrieves specific columns from a table. - **Example**: ```sql SELECT Name, Salary FROM Employees; ``` - **NATURAL JOIN**: Combines rows from two tables based on common columns with the same name. - **Example**: ```sql SELECT * FROM Employees NATURAL JOIN Departments; ``` - **UNION**: Combines the result sets of two queries, removing duplicates. - **Example**:  ```sql SELECT Name FROM Employees UNION SELECT Name FROM Managers; ``` - **CARTESIAN PRODUCT (×)**: Returns the Cartesian product of two tables, combining each row from the first table with each row from the second table. - **Example**: ```sql SELECT * FROM Employees CROSS JOIN Departments; ``` 46. **Consider the following schema and represent given statements in relational algebra form.** - **Schema**: - `Branch(branch_name, branch_city)` - `Account(branch_name, acc_no, balance)` - `Depositor(Customer_name, acc_no)` - **Queries**: - **(i) Find out list of customers who have accounts at ‘abc’ branch**:  ```sql σ_branch_name='abc'(Account) ⨝ Depositor ``` - **(ii) Find out all customers who have accounts in ‘Ahmedabad’ city and balance is greater than 10,000**: ```sql σ_balance > 10000 (Account ⨝ σ_branch_city='Ahmedabad'(Branch)) ⨝ Depositor ``` - **(iii) Find out list of all branch names with their maximum balance**: ```sql π_branch_name, MAX(balance) (Account) ``` 47. **Describe the Set operation works in relational algebra.** - **Set Operations**: Operations that work on relations to combine or compare sets of tuples. - **Types**: - **UNION**: Combines tuples from two relations, removing duplicates. - **Example**: ```sql R1 ∪ R2 ``` - **INTERSECTION**: Returns tuples that are present in both relations.  - **Example**: ```sql R1 ∩ R2 ``` - **DIFFERENCE**: Returns tuples present in the first relation but not in the second. - **Example**: ```sql R1 - R2 ``` - **PRODUCT**: Returns the Cartesian product of two relations. - **Example**: ```sql R1 × R2 ``` These operations are foundational for querying and manipulating data in relational databases. ### Short Questions 48. **Define functional dependency. Explain trivial and non-trivial FD with example.** - **Functional Dependency (FD)**: A relationship between two sets of attributes in a relation. Attribute `X` functionally determines attribute `Y` if for each value of `X`, there is a single corresponding value of `Y`. It is denoted as `X → Y`. - **Trivial Functional Dependency**: An FD is considered trivial if the dependent attributes are a subset of the determinant attributes. In other words, `X → Y` is trivial if `Y` is a subset of `X`. - **Example**: - For `A → A`, this is trivial because `A` is a subset of itself. - **Non-Trivial Functional Dependency**: An FD is non-trivial if the dependent attributes are not a subset of the determinant attributes. In other words, `X → Y` is non-trivial if `Y` is not a subset of `X`. - **Example**: - For `A → B` where `B` is not a subset of `A`, this is non-trivial. 49. **What do you mean by Functional Dependency?** - **Functional Dependency**: It is a constraint between two sets of attributes in a relational database. Attribute `X` functionally determines attribute `Y` if and only if for every unique value of `X`, there is a single corresponding value of `Y`. It describes how attributes in a relation depend on each other. ### Long Questions 50. **Given relation R with attributes A, B, C, D, E, F and set of FDs as A → BC, E → CF, B → E, and CD → EF. Find out the closure of FD.**  To find the closure of a functional dependency, we determine all the attributes that can be functionally determined by a given set of attributes. - **Given FDs**: 1. `A → BC` 2. `E → CF` 3. `B → E` 4. `CD → EF` - **Closure Calculation**: Let's find the closure of the attribute set `{A, C, D}`: 1. Start with `{A, C, D}`. 2. Apply FD `A → BC`: - From `A`, we get `B` and `C`, so now we have `{A, B, C, D}`. 3. Apply FD `B → E`: - From `B`, we get `E`, so now we have `{A, B, C, D, E}`. 4. Apply FD `E → CF`: - From `E`, we get `C` and `F`. Since `C` is already in our set, we just add `F`, so now we have `{A, B, C, D, E, F}`. 5. Apply FD `CD → EF`: - We already have `C` and `D`, so we can add `E` and `F`, but they're already included in our set. - **Closure**: The closure of `{A, C, D}` is `{A, B, C, D, E, F}`. 51. **What is inference rules/Armstrong's axioms?** - **Inference Rules (Armstrong's Axioms)**: A set of rules used to infer all the functional dependencies that are logically implied by a given set of FDs. Armstrong's axioms include: 1. **Reflexivity**: If `Y ⊆ X`, then `X → Y`. 2. **Augmentation**: If `X → Y`, then `XZ → YZ` for any `Z`. 3. **Transitivity**: If `X → Y` and `Y → Z`, then `X → Z`. These axioms are used to derive all possible functional dependencies in a relation based on the given set of FDs. 52. **Let R = (A, B, C, D, E, F) be a relation scheme with the following dependencies: C → F, E → A, EC → D, A → B. Find the closure of FD.** - **Given FDs**: 1. `C → F` 2. `E → A` 3. `EC → D` 4. `A → B` - **Closure Calculation**: Let's find the closure of the attribute set `{E, C}`:  1. Start with `{E, C}`. 2. Apply FD `C → F`: - From `C`, we get `F`, so now we have `{E, C, F}`. 3. Apply FD `E → A`: - From `E`, we get `A`, so now we have `{E, C, F, A}`. 4. Apply FD `A → B`: - From `A`, we get `B`, so now we have `{E, C, F, A, B}`. 5. Apply FD `EC → D`: - We already have `E` and `C`, so we can add `D`, so now we have `{E, C, F, A, B, D}`. - **Closure**: The closure of `{E, C}` is `{E, C, F, A, B, D}`.