Set Theory as a Framework for Relational Databases

 

A set can be a collection of any type of object, ranging from people to places to things. Basic set theory includes the study of subsets, proper subsets, finite and infinite sets, and the logical operations on them. Set theory plays a foundational role in mathematical processes and ideas and also has connections to computer engineering, programming, and databases.

The relational database model, originally invented by computer scientist Edgar F. Codd in 1969, is based on ideas from set theory. A simple database is a collection of records stored in tables. A relational database also includes relationships stored across multiple tables. One can run queries on the relational database to request specific information with set theory operators, such as union and intersection.

Post 1: Initial Response

Imagine you are responsible for your organization’s analytic tasks, and you are currently brainstorming how to query a relational database of marketing information for the organization. You want to test your understanding of how you might relate the database tables with the use of set theory, and particularly subsets. To carry out your test, complete each of the following:

To define two sets, set A and set B, first conduct an online browsing trial, in which you spend 10–20 minutes looking at different websites, such as for national news, social media, sports, hobbies, recipes, etc. Let set A represent exactly three distinct company names from any online advertisements you saw during your browsing trial. Let set B represent at least three distinct company names for any online retailers you have purchased from in the past year.
To prepare to use your algorithm, answer the following questions:
How many elements are in set A? This is what you will set as m = ___.
How many elements are in set B? This is what you will set as n = ___.
What are your first and last elements of A? Show these as a[1] = ____ and a[m] = ___.*
What are your first and last elements of B? Show these as b[1] = ____ and b[n] = ___.*
*Note: Recognize that there are other elements you will cycle through as you trace the algorithm. While you are not required to list all elements in this form, you will need to use them, in addition to the first and last elements, as you complete your trace.

Using your sets A and B along with what you just outlined to prepare, determine an algorithm that you can use to see whether A ⊆ B.
State the algorithm that you would use to compare these sets.
Based on your algorithm, did you find that A ⊆ B or that A ⊈ B? Explain. If A ⊈ B, how are they related (e.g., disjoint, intersecting)?
View Unit 6 Discussion Post 1 example.

Post 2: Reply to a Classmate

Now you want to try out the algorithm on another person’s data to further test your understanding and bolster your confidence about assessing relations computationally as you approach this relational database project.

Review a classmate’s post and consider their set B. Address the following items completely.

Using your set A and their set B determine whether A ⊆ B or that A ⊈ B? Explain how you know this. If A ⊈ B, how are they related (e.g., disjoint, intersecting)?
How might the understanding you have gained from your Post 1 and Post 2 tests be useful if you were responsible for querying a relational database?
View Unit 6 Discussion Post 2 example.

Post 3: Reply to Another Classmate

After conducting this computational practice, you have begun to develop some technical insight into how you might investigate and seek information on the marketing habits of clients by querying a relational database. However, you know your fellow staff members are not interested in this technical insight. So, for your general meeting, you plan to present a visual synopsis of some ideas considered in the planning stages of this project.

Review another classmate’s post and consider their sets A and B. Address the following items completely.

Create a Venn diagram that models all of the elements in your classmate’s sets A and B. Carefully place elements appropriately in the intersecting versus non-intersecting areas representing sets A and B, respectively. You may use the software of your choice for the Venn diagram (e.g., creatly.com, cosketch.com, Microsoft® Word®, or PowerPoint®). Copy and paste the image or screenshot of your Venn diagram into your post. (You may also use an attached file if needed.)
Draft some talking points in anticipation of addressing the following questions during your presentation:
How do these two sets relate in the example illustrated by the Venn diagram?
How have the concepts of sets and set operations been utilized in your analytic tasks?
How might table relationships be modeled from the ideas of set theory?

 

Sample Solution

ntaminants into the climate, which imperils the occupants. Unfortunate air quality has been the cost paid for urbanization; Populace, Modern exercises, Farming and so on. As per WHO, in 2012 around 6.5 million passings which is 11% of worldwide passings were because of open air and indoor air contamination, with 90% event in low and center pay nations. The dangers related with metropolitan air contamination has been known for a significant stretch of time, however up to this point preliminaries, to moderate them has become more perplexing than any other time. In the past air contamination was for the most part connected with created nations, however today research has shown that emerging nations have more air quality issues (Fenger, 2009).

In 2015, the little Green information book detailed that the Nigerian populace is presented to elevated degrees of Particulate matter(PM) 2.5 which surpasses the ordinary norms/rules set by WHO at 94%, and it went further to express that 3% of kids under 5 years old experienced intense respiratory disease. Particulate Matter contamination is turning into a major issue universally particularly for low and center pay nations. It affects people, climate and air conditions. (Pope and Dockery 2006; Taiwo et al., 2014)

A later report from WHO makes sense of that 97% of low and center pay nations and 47% of big time salary nations have horrendous air quality credited to Particulate Matter, which seriously endangers the number of inhabitants in these nations of cellular breakdown in the lungs, persistent and intense respiratory illnesses, stroke, and heart sicknesses.

WHO (2016) detailed that Onitsha is the most obviously terrible air dirtied city on the planet, because of its elevated degree of Particulate Matter (PM) 10 which was multiple times more than the suggested fixation as set by WHO. (See informative supplements 1, 2, 3). A few examinations in the past have attempted to resolve the issue of air contamination in Onitsha; distinguishing the different patrons of PM, for example, transportation, modern exercises, poor metropolitan arranging and so on. (Nwankwo, 2017). Insufficient examinations has been finished about the issue of PM contamination in Onitsha. An air quality screen in Onitsha recorded 594 and 66 miniature life forms for each cubic meter of PM 10 and 2.5 separately. Albeit this data was respected not so dependable by WHO agent, as a result of the presence of only one single observing station in the city. The ongoing accentuation is on PM 10 in Onitsha presently yet it would likewise be important to focus on PM2.5 additionally, in light of the fact that it has been connected to medical conditions like flu (Feng et al., 2016) and numerous others.

Onitsha is situated in Anambra, Southeastern Nigeria, with a populace of 1,417,711 as detailed by Fagbeja et al., (2017). It is situated on scope 6.1°N and longitude 6.8°E in the Anambra North Senatorial Zone of Anambra State. The city is partition into Onitsha south and Onitsha North neighborhood governm

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