# 15 Lecture

## CS403

### Midterm & Final Term Short Notes

## Database and Math Relations

Database and math relations are closely connected as both involve the use of sets, relations, and functions. In mathematics, a relation is a set of ordered pairs, while in a database, a relation is a table with rows and columns. The concepts of

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**What is a relation in mathematics?**a) A set of ordered pairs b) A table with rows and columns c) A mathematical function d) A data type Answer: a) A set of ordered pairs**What is a relation in a database?**a) A set of ordered pairs b) A table with rows and columns c) A mathematical function d) A data type Answer: b) A table with rows and columns**What is the purpose of domain and range in a relation?**a) To specify the types of data that can be stored in a table b) To specify the primary key of a table c) To specify the columns of a table d) To specify the input and output values of a function Answer: d) To specify the input and output values of a function**What is the cardinality of a relation?**a) The number of rows in a table b) The number of columns in a table c) The number of ordered pairs in a relation d) The number of tables in a database Answer: c) The number of ordered pairs in a relation**Which of the following mathematical concepts is used in database design?**a) Set theory b) Geometry c) Trigonometry d) Calculus Answer: a) Set theory**Which of the following is not a relational database management system?**a) MySQL b) Oracle c) MongoDB d) PostgreSQL Answer: c) MongoDB**What is the purpose of SQL?**a) To design web pages b) To program software applications c) To manipulate data in a database d) To create computer graphics Answer: c) To manipulate data in a database**What is a primary key in a table?**a) A field that references the primary key of another table b) A unique identifier for a record in a table c) A virtual table in a database d) A field that is used to store text data Answer: b) A unique identifier for a record in a table**What is the purpose of a foreign key in a table?**a) To establish a relationship between two tables b) To restrict access to sensitive data c) To perform calculations on data in a table d) To store images or other media files Answer: a) To establish a relationship between two tables**Which of the following is an advantage of using a database?**a) Data redundancy b) Data inconsistency c) Improved data security d) Limited scalability Answer: c) Improved data security

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**What is the relationship between sets and relations in mathematics?**Answer: Sets and relations are closely related in mathematics, as a relation is a set of ordered pairs that relate elements from two or more sets.**How is the concept of cardinality used in database design?**Answer: Cardinality is used to specify the number of elements that can be present in a relationship between two tables in a database.**What is the purpose of the primary key in a table?**Answer: The primary key is used to uniquely identify each record in a table and is an important part of ensuring data consistency and accuracy.**What is normalization in database design?**Answer: Normalization is the process of organizing data in a database to reduce redundancy and improve data consistency.**How is the concept of functions used in database design?**Answer: Functions are used in database design to perform calculations and manipulate data in tables.**What is the difference between a one-to-many and a many-to-many relationship in database design?**Answer: A one-to-many relationship indicates that each record in one table can have multiple corresponding records in another table, while a many-to-many relationship indicates that each record in both tables can have multiple corresponding records in the other table.**What is the purpose of foreign keys in a table?**Answer: Foreign keys are used to establish relationships between tables in a database and are a key component of data integrity.**How is the concept of set theory used in database design?**Answer: Set theory is used to model relationships between data in a database and to ensure data consistency and accuracy.**What is the role of SQL in database management?**Answer: SQL is a programming language used to manipulate and manage data in a database.**How can a database be used to improve data security?**Answer: A database can be used to restrict access to sensitive data and to track changes and access to data over time.