## Mathematics

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, by applying Algorithm 6.1.1. 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 3 distinct company names from any online advertisements you saw during your browsing trial. Let set B represent at least 3 distinct company names for any online retailers you have purchased from in the past year.
To prepare to use the 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, trace the action of Algorithm 6.1.1, and present your trace table.
Based on your trace, did you find that A ⊆ B or that A ⊈ B? Explain. If A ⊈ B, how are they related (e.g., disjoint, intersecting)?