All questions of Concept of keys for Computer Science Engineering (CSE) Exam

Understanding Primary Keys and Relations
In relational database management systems, the concept of primary keys and their relationships is fundamental for maintaining data integrity and establishing connections between different tables.
Primary Key Definition
- A primary key is a unique identifier for each record in a database table.
- It ensures that no two rows have the same key value, which helps in uniquely identifying each entry.
Referenced Relation Explained
- The term "referenced relation" pertains to the table that contains the primary key being referenced by another table.
- This relationship forms the backbone of relational databases, where one table (the referencing relation) points to another (the referenced relation) to establish a link between data.
Referencing vs. Referenced Relation
- The referencing relation is the table that includes a foreign key, which is a field that links back to the primary key in another table.
- The referenced relation (correct answer) is the table that contains the primary key that is referred to by the foreign key in the referencing table.
Example for Clarity
- Consider two tables: `Employees` and `Departments`.
- `Employees` has a primary key `EmployeeID`, while `Departments` may include a foreign key `DepartmentID` that references the `DepartmentID` in `Departments`.
- Here, `Departments` is the referenced relation because it contains the primary key that `Employees` refers to.
Conclusion
Understanding the distinction between referencing and referenced relations is crucial for designing efficient database schemas and ensuring data integrity across related tables. The referenced relation serves as the source of truth for the primary key that other tables depend on for their foreign keys.

The fundamental operations of relational algebra include selection, projection, union, set difference, Cartesian product, and rename. Set intersection and natural join are not considered fundamental operations but can be derived from these fundamental operations.

Understanding Minimal Super Keys
In relational databases, the concept of keys is fundamental for establishing relationships between tables and ensuring the integrity of data. Among these keys, candidate keys hold significant importance.
What are Candidate Keys?
- A candidate key is a minimal super key, meaning it is a set of attributes that can uniquely identify a tuple (row) in a relation (table).
- Minimality implies that if any attribute is removed from the candidate key, it will no longer uniquely identify the tuples.
- Each candidate key can serve as a potential primary key for the table.
Characteristics of Candidate Keys:
- Uniqueness: Each value of a candidate key must be unique across the table.
- Irreducibility: No subset of the candidate key can uniquely identify the tuples in the table.
- Multiple Candidates: A table may have multiple candidate keys, but one of them is selected as the primary key.
Examples of Candidate Keys:
- In a student database, attributes like StudentID or a combination of (FirstName, LastName, DOB) could serve as candidate keys, provided they are unique.
Why Candidate Keys Matter:
- Data Integrity: They ensure that no two records are the same based on the key attributes.
- Efficiency: They optimize queries and improve database performance by indexing unique identifiers.
In summary, the correct answer to the question regarding minimal super keys is option 'B' - Candidate keys. They are critical for maintaining the structure and reliability of relational databases.

Understanding Domain in Database Relations
In the context of databases, particularly in relational database design, the concept of "domain" is fundamental. Here’s a detailed explanation of why the correct answer is option 'A'.
Definition of Domain
- The domain of an attribute is defined as the set of permissible values that the attribute can take.
- Each attribute in a relation (or table) is associated with a specific domain that constrains the values that can be stored in that attribute.
Importance of Domain
- Data Integrity: Domains ensure that the data entered into the database is valid and consistent. For example, if an attribute is defined to hold integers, the domain restricts entries to integer values only.
- Type Safety: By defining domains, databases enforce type safety. This means that operations performed on the data are appropriate for the data type, reducing errors and enhancing reliability.
Example of Domain
- Consider a database for a library:
- The "Publication Year" attribute might have a domain of years from 1450 to the current year.
- The "Book Title" attribute would have a domain of string values, allowing any sequence of characters.
Conclusion
- By establishing domains for attributes, a relational database maintains high standards of data quality and integrity.
- Therefore, the correct answer to the question is indeed option 'A' — the domain of an attribute is crucial for defining what values are permissible within that attribute.

A foreign key in a relation is an attribute that is a primary key in another relation. This key ensures referential integrity between the two relations. For example, in a "Student" table, "DepartmentID" could be a foreign key referencing the "DepartmentID" in a "Department" table.

A super key is a set of one or more attributes that, taken collectively, can uniquely identify a record in a table. This includes primary keys, candidate keys, and any superset of them. For example, in a table of students, the combination of student ID and email could serve as a super key.

The selection operation in relational algebra is denoted by the Greek letter Sigma (σ). It is used to select tuples that satisfy a given predicate, such as σ_age > 30 (Employee).

Relational algebra is a procedural query language, meaning it specifies a sequence of operations to perform on relations to achieve the desired result. It involves operations like selection, projection, and join that manipulate relations and produce a new relation.

A key is a property of the entire relation, ensuring that each tuple (row) in the relation is unique. This is fundamental to the concept of relational databases, where keys ensure the uniqueness and integrity of data. For instance, a primary key in a table uniquely identifies each record.

A candidate key is a minimal super key, meaning no proper subset of it can be a super key. If any subset of the super key is still a super key, it cannot be minimal. For instance, if {A, B} is a super key, neither {A} nor {B} alone can be a super key for it to be a candidate key.

In the select operation, predicates (conditions) are written in the subscript, and the relation (table) to which these conditions apply is written in the parenthesis after the Sigma (σ). For example, σ_salary > 5000(Employee).