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Closure of Functional Dependencies
A functional dependency in a relational database is the constraint defining the
relationship between two attributes. Setting the functional dependencies of a database system
beforehand is imperative, as it influences the schema design of a relational database (Link &
Prade, 2019). The closure of a functional dependency; thus, is the limit of the attributes for which
a functional dependency, F, holds true. That is, the closure defines the set of attributes within the
bounds of a given functional dependency. In the example of F, its closure would be, as
articulated by Elmasri and Navathe “all functional dependencies that can be inferred” (p. 506).
The closure may as well be defined as the scope of functional dependency. The complete set of
possible attributes for F, are presented as {F}+, a connotation which equates to the corresponding
functional dependencies. It is important to note that dependencies need not be explicitly stated.
Rather, they may be inferred based on the relations among other secondary functions. The
definitions offered above are best understood through an illustration.
Consider a scenario in a work environment, whereby there is only one IT expert per
department (dep_id). The relationship between the IT expert and the department is; thus, explicit.
Imagine then, that all employees in the work context have a unique ID (emp_id). As department
implies the IT expert, written as; dep_id → emp_id, then another unique quality of the IT expert
may be inferred from the department ID. Taking this further, it may be assumed that, each
employee has a designated workplace phone number (phn_id), a situation that could be
represented as; emp_id → phn_id. As such, a relationship between the department an IT expert
belongs to, and the phone number of the said employee could be inferred as; dep_id → phn_id.
The attribute phn_id; hence, is functionally dependent on the department of the corresponding
employee. The abbreviated denotation of the relationship would be presented as {dep_id}+ =
{emp_id, phn_id}.
A summation of a relation with functional dependencies is below. A relation R, with
attributes A, B, C, D, E can be shorthanded as; R (A, B, C, D, E). Assuming some attributes in
the relation have functional dependencies where, A implies B and C, C implies B and D, and
both D and E imply and are implied by one another, the functional dependencies would be
denoted as A → B, C; C → B, D; D → E; and E → D. The closure of the functional
dependencies would be;
{A}+ = {B, C}
{C}+ = {D, E}
{D}+ = {E}
{E}+ = {D}
Hence, the above representation defines the closure of R’s functional dependencies.
Elmasri, R., & Navathe, S. B. (2015). Relational Database Design Algorithms and Further
Dependencies. In Fundamentals of Database Systems (pp. 503 – 537). Pearson.
Link, S., & Prade, H. (2019). Relational database schema design for uncertain data. Information
Systems, 84, 88-110.
Reply to 2 Discussion Posts (Ch15)
Please “Reply” to the below TWO discussion posts. I have attached 2 “Discussion Posts” in this
document, and you only need to reply to them. Please note that this is a “Reply” assignment which might
achieve some of the following,
Ask an interesting, thoughtful question pertaining to the topic
Share an applicable personal experience
Provide an outside source
Make an argument
Robert__F, to give some context, please note that the discussion questions (in the below posts) were
already answered by you previously, and this (“Reply” assignment) is a reply to the discussion questions
(in the below posts) which was answered by other students. I have attached your previous answers
which might help you with the reply.
Your reply needs to be about 100 words per reply. Total of about 200 words for the two
Use at least ONE quality scholarly (peer reviewed) sources per reply.
Ensure to provide the DOI / URL for all references.
Discussion Post #1
Discussion (Chapter 15):
What is meant by the closure of a set of functional dependencies? Illustrate with and example.
FUNCTION Operation
The set of rules used or stipulated for solving functions is known as function operations. A function
operation, often known as an aggregate function, performs various mathematical aggregate functions on numeric
data (Elmasri & Navathe, 2017). Another approach to conceiving an equation with an x and y value is a function.
Consider x as the input value or the value we enter into the equation to receive the outcome. Similarly, we may
consider y the output value or the outcome of plugging x into the equation. It also allows data to be grouped based
on various relational features (Setiaji & Wibowo, 2016). These principles include specifications, especially when
working with addition, subtraction, divisions, and multiplication of functions.
Functions are useful when the same process must be done several times or in multiple locations. Instead of writing
the same set of queries many times, we may write one function and call it from various places. Functions are
commonly employed in math and arithmetic, particularly in algebraic structures and discrete mathematics; they are
also useful in solving basic operations like matrices and equations (Elmasri & Navathe, 2017). We are accustomed
to performing the four fundamental arithmetic operations with integers and polynomials: addition (f+g), subtraction
(f-g), multiplication (f.g), and division of functions (f/g). Most thermometers include degrees of Fahrenheit and
Celsius, which is a practical illustration of function operations in the real world. Learners can freely interpret the
results of these thermometers owing to the calibrations. The temperature function may be used to compute a room
or body temperature, either an in-room or standard temperature.
Elmasri, R., & Navathe, S. B. (2017). Fundamentals of Database Systems 7 th Edition.
Setiaji, B., & Wibowo, F. W. (2016). Chatbot using a knowledge in database: human-to-machine conversation
modeling. In 2016 7th international conference on intelligent systems, modelling and simulation
(ISMS) (pp. 72-77). IEEE.
Discussion Post #2
Discussion (Chapter 15):
What is meant by the closure of a set of functional dependencies? Illustrate with and example.
The Function is an operation used in a database system for storing temporary data structures in a
transaction, where the temporary data is used to store other temporary data elements. The Function’s Name is a text
representation of the Function’s Name. The Name of a relation or column in a table or table index is descriptive.
The Function’s Description is a text representation of a description of a function. Each description includes a
description of the data (as well as a function name, Name of its arguments, and result type) that goes with the
description. You can specify a description in your specification. An example of the type of data to describe is a
function parameter. You can specify the function name (function name in this case), the function arguments, and
their return type. The return type indicates the type of data retrieved from the returned objects (Deng et al., 2022).
Function usage is a problem that leads to the design of functions, which may introduce the following
problems: Complexity, which is a requirement in architecture to keep the functionality of a system in line with its
user’s needs. Cost is an essential element for the selection of a suitable platform in order to pay for the amount of
time and money necessary to make the necessary changes. Interoperability problems are an essential factor for the
success of the software, especially when the software is integrated with different networks to allow the users of the
communication system to exchange information about each other. Some of the aspects in this category involve
interoperability issues and security features. The security features can range from simple authentication and
encryption to complex authentication and encryption methods (Deng et al., 2022).
This section gives the basic rules, which we can use when implementing database systems for different
application domains: All database objects should have a referential integrity type. No duplicate objects should exist
in the database. All database objects should have a security key attribute. If an object has a security key, it must
have a unique access control list (ACL) value. The access permissions must be assigned to each object with its
ACL value. An object’s default method of operation and security descriptor are both ACL values. An object’s
Security Descriptor is the object’s Security Type. Security Descriptor value and Object type have an associated
Object DACL value. A security descriptor is a set of fields-or groups of fields part of the object’s security
descriptor. The following types of security descriptors are supported: Identifier-A field that identifies a set of object
properties (Abd Alsammed, 2022).
Abd Alsammed, S. M. Z. (2022). Advanced GIS-based Multi-Function Support System for Identifying the Best
Route. Baghdad Science Journal, 19(3), 0631-0631.
Deng, N., Wu, C., Yaseen, A., & Wu, H. (2022). ImmuneData: an integrated data discovery system for
immunology data repositories. Database, 2022.

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