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 organizations 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 1020 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] = ___.*

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. You can make your own or find one somewhere else.

- State the algorithm that you would use to compare these sets. If you are using an algorithm that you did not write, cite or describe where you found it.
- 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)?
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- Post 2: Reply to a Classmate

- Now you want to try out the algorithm on another persons data to further test your understanding and bolster your confidence about assessing relations computationally as you approach this relational database project.
- Review a classmates post and consider their set B. Address the following items completely.
- Using your set A and their set B, use the algorithm they described to determine whether A ? B or 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?

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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 classmates 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 classmates 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?

**Set Theory as a Framework for Relational Databases**

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