NCERT Solutions Class 12 Computer Science Chapter 8 Database Concepts

What is relation? Define the relational data model.

A relation is a table having atomic values, unique rows, and unordered rows and columns. Each relation represents an entity and contains information about that entity.

The relational data model represents data and relationships among data by a collection of tables known as relations, each of which has a number of columns with unique names. Key features include:

• Data is stored in tables (relations)
• Each table has rows (tuples) and columns (attributes)
• Each column has a unique name
• All values in a column are of the same data type
• Each row is unique
• Order of rows and columns is immaterial

What are all the domain names possible in gender?

The possible domain names for gender are:

• Male
• Female

In database terminology, a domain defines the set of possible values that an attribute can contain. For the gender attribute, the domain is restricted to these two values to maintain data consistency and integrity.

Give a suitable example of a table with sample data and illustrate Primary and Candidate Keys in it.

Candidate Keys: A table may have more than one attribute or group of attributes that identifies a row/tuple uniquely. All such attributes are known as Candidate Keys.

Primary Key: Out of the Candidate keys, one is selected as Primary Key.

Differentiate between cardinality and degree of a table with the help of an example.

Cardinality: The number of rows (tuples) in a table.
Degree: The number of columns (attributes) in a table.

Observe the following table carefully and write the names of the most appropriate columns, which can be considered as (i) candidate keys and (ii) primary key.

Based on the table analysis:

• Candidate keys: Id, Product
• Primary key: Id

Explanation: Both Id and Product can uniquely identify each row in the table, making them candidate keys. Id is chosen as the primary key as it's typically more stable and efficient for database operations.

Observe the following table carefully and write the names of the most appropriate columns, which can be considered as (i) candidate keys and (ii) primary key:

Based on the table analysis:

• Candidate keys: Code, Item
• Primary key: Code

Explanation: Both Code and Item attributes can uniquely identify each record in the table, making them candidate keys. Code is selected as the primary key as it's typically more efficient for indexing and referencing.

Define degree and cardinality. Based upon given table write degree and cardinality.

Definitions:

• Degree: The number of attributes or columns present in a table.
• Cardinality: The number of tuples or rows present in a table.

Differentiate between the Primary key and Alternate key of a table with the help of an example.

Primary Key: A primary key is a value that can be used to identify a unique row in a table. It cannot be null and must be unique.

Alternate Key: An alternate key is any candidate key which is not selected to be the primary key.

Explain the concept of candidate keys with the help of an appropriate example.

Candidate Key: A candidate key is a column or set of columns that can help in identifying records uniquely in a table. A table may have multiple candidate keys.

A table customer has 10 columns but no row. Later, 10 new rows are inserted and 3 rows are deleted in the table. What is the degree and cardinality of the table customer?

Step-by-step calculation:

• Initial state: 10 columns, 0 rows
• After inserting 10 rows: 10 columns, 10 rows
• After deleting 3 rows: 10 columns, 7 rows

Note: Degree represents the structure of the table (columns) and doesn't change unless columns are added or removed. Cardinality represents the data in the table (rows) and changes when rows are inserted or deleted.

A table student has 3 columns and 10 rows and another table student2 has the same number of columns and 15 rows. 5 rows are common in both the tables. If we take union, what is the degree and cardinality of the resultant table?

Given:

• Table student: 3 columns, 10 rows
• Table student2: 3 columns, 15 rows
• Common rows: 5

Union Operation: The union operation combines all unique rows from both tables, eliminating duplicates.

Note: The degree remains the same as both tables have the same structure. The cardinality is calculated by adding all rows and subtracting the duplicates.

A table student has 4 columns and 10 rows and table student2 has 5 columns and 5 rows. If we take Cartesian product of these two tables, what is the degree and cardinality of the resultant table?

Given:

• Table student: 4 columns, 10 rows
• Table student2: 5 columns, 5 rows

Cartesian Product: The Cartesian product combines every row of the first table with every row of the second table.

Formula:
Degree of result = Degree of Table1 + Degree of Table2
Cardinality of result = Cardinality of Table1 × Cardinality of Table2

Observe the following table and answer the parts (i) and (ii):

1. In the above table, can we have Qty as primary key? [Answer as yes/no]. Justify your answer.
2. What is the cardinality and degree of the above table?

1. Can Qty be used as primary key?

2. Cardinality and Degree:

Key Point: A primary key must have unique, non-null values. Any column with duplicate values cannot serve as a primary key.

What do you understand by Union & Cartesian product in the relational algebra?

Union Operation (∪):

Cartesian Product (×):

Explain the concept of union between two tables, with the help of appropriate example.

The union operation denoted by ∪ combines two or more relations. The resultant of union operation contains tuples that are in either of the tables or in both tables, with duplicates eliminated.

In the following 2 tables, find the union value of Student1 and Student2.

To find the union of Student1 and Student2 tables, we need to:

1. Combine all rows from both tables
2. Remove any duplicate rows
3. Ensure both tables have the same structure (same number and type of columns)

Note: The specific union result would depend on the actual data shown in the referenced image. The union will contain all unique combinations of values from both tables.

Observe the table Club given below:

1. What is the cardinality and degree of the above given table?
2. If a new column contact no has been added and three more members have joined the club then how these changes will affect the degree and cardinality of the above given table.

1. Current table characteristics:

2. After changes:

In which situation can we apply union operation of two tables?

Union operation between two tables can be applied when the following conditions are met:

Note: The union operation automatically eliminates duplicate rows from the result, ensuring each unique combination of values appears only once.

Observe the following STUDENTS and EVENTS tables carefully and write the name of the RDBMS operation which will be used to produce the output as shown in LIST. Also, find the Degree and Cardinality of the LIST.

RDBMS Operation: Cartesian Product (×)

Explanation: The Cartesian product operation combines every row from the STUDENTS table with every row from the EVENTS table. This creates a new relation where:

• Each student is paired with each event
• The result contains all possible combinations
• No filtering or matching conditions are applied

Observe the following PARTICIPANTS and EVENTS tables carefully and write the name of the RDBMS operation which will be used to produce the output as shown in RESULT. Also, find the Degree and Cardinality of the RESULT.

RDBMS Operation: Cartesian Product (×)

Process: The Cartesian product operation creates a comprehensive combination where:

• Every participant is matched with every event
• All attributes from both tables are included
• The operation generates all possible pairings