Discrete Mathematics
· The Assessment 1 Context document contains additional information about the concepts and language of sets, functions, sequences, and relations and their application to relational databases.
Resources
Suggested Resources
The following optional resources are provided to support you in completing the assessment or to provide a helpful context. For additional resources, refer to the Research Resources and Supplemental Resources in the left navigation menu of your courseroom.
Capella Resources
Click the links provided to view the following resources:
Capella Multimedia
Click the links provided below to view the following multimedia pieces:
· Functions and Relations | Transcript.
2. This presentation introduces the following topics.
1. Functions.
1. Modulus operator.
1. One to one functions.
1. Onto functions.
1. Composite functions.
1. Sequences.
1. Sigma notation.
1. Relations.
1. Order relations.
Library Resources
The following e-book from the Capella University Library is linked directly in this course:
· Koshy, T. (2004). Discrete mathematics with applications . Burlington, MA: Elsevier Academic Press.
. Chapters 2, 3, and 7.
Course Library Guide
A Capella University library guide has been created specifically for your use in this course. You are encouraged to refer to the resources in the MAT-FP2051 – Discrete Mathematics Library Guide to help direct your research.
Bookstore Resources
The resource listed below is relevant to the topics and assessments in this course and is not required. Unless noted otherwise, this resource is available for purchase from the Capella University Bookstore. When searching the bookstore, be sure to look for the Course ID with the specific –FP (FlexPath) course designation.
· Johnsonbaugh, R. (2018). Discrete mathematics (8th ed.). New York, NY: Pearson.
. Chapter 3, “Functions, Sequences, and Relations,” is particularly useful for your work in this assessment. In addition to focusing on functions, sequences, and relations, this chapter discusses equivalence relations, matrices of relations, and relational databases.
· Assessment Instructions
Imagine your company asks you to organize a relational database containing employee information. A database has entries represented by rows and fields represented by columns. An entry corresponds to each employee, and each employee has various characteristics depicted by each field. In this database, you will store information for the following six fields for each employee: firstName, lastName, SS#, age, yearsAtCompany, and phoneNumber. Complete the following:
· In general, entries in a relational database can be represented as a set of n-tuples, where n is the number of fields. Provide 3 sample entries from 3 employees in the company. Feel free to devise their personal information in each field. Write out this information as a set of 3 6-tuples.
· Since the database has 6 fields and is represented as a set of 6-tuples, it is considered an n-ary relation where n=6. Let us focus in on two fields of our database: firstName and lastName. Given these two fields, we can define a binary relation, represented by the set of 2-tuples, which includes all entries in our database of these two fields. Note: The first entries in the 2-tuples represent elements from the domain, and the second entries in the 2-tuples represent elements from the range. Assume you have populated this database with all employee information. Do you believe this binary relation would be symmetric, transitive, and/or reflexive? Justify your answers. Feel free to use examples to help justify.
· In general, a function is a specific type of relation such that each element in the domain is related to exactly one element of the range. Given the binary relation composed by the fields firstName and lastName, is this relation a function? Justify your answer.
· In the context of databases, a key is a field in the database with the particular characteristic that each value in this field is related to only 1 entry (row) in the database. It is a unique identifier. Given this database, which field would be the best key? Justify your answer.
· Using 2 of the fields from this database, describe a binary relation such that the relation is a function. Define the domain and the range of this function. Describe this function onto (surjective), one-to-one, (injective), or both (bijective). Justify your answer. Feel free to use an illustration to aid in explanation.