below is the link to the textbook that i want you to use for reference incase you many need

https://ccsf-math-115.github.io/textbook/mcs_2018_…

# Category: Discrete Math

Rewrite the solution by using the mathematical induction method.

Refer to the lecture notes

24 – Lecture notes 11/08/2022

25 – Lecture notes 11/15

The solution is on the lecture notes 25. However, you need to rewrite the solutions in detail.

Rewrite the solution by using the mathematical induction method.

Refer to the lecture notes

24 – Lecture notes 11/08/2022

25 – Lecture notes 11/15

The solution is on the lecture notes 25. However, you need to rewrite the solutions in detail.

Imagine a real-world situation that involves relationships that can be modeled with a graph. A graph consists of a discrete number of vertices and the edges that connect them. When brainstorming the situation you would like to model with a graph, review the examples that have been presented in your unit readings and homework exercises for ideas.

Consider a situation in your personal or professional world that involves relationships that can be modeled with a graph. Describe this situation in at least one well-composed paragraph, sharing:

A brief description of the situation modeled,

What each vertex represents, and

What each edge represents.

Draw a connected graph using a drawing program of your choice and include it in your post. The following must be present in your graph:

5–10 vertices, each clearly labeled with a single capital letter (A, B, C, D, E …)

At least 2 vertices of degree 3 or more (the degree of a vertex is the count of how many edges are attached to that vertex).

At least 1 circuit.

Set Theory as a Framework for Relational Databases

An Example of How Post Should Be Done is Attached

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)?

Set Theory as a Framework for Relational Databases

An Example of How Post Should Be Done is Attached

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)?

## How many elements are in set b?

Set Theory as a Framework for Relational Databases

An Example of How Post Should Be Done is Attached

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)?

2 Peer Posts have been provided in the attached Word Document. Following the Directions below, and following the examples, I need a response for each of these posts. There must be one of each type of response, as outlined in the instructions below. Post 2: Reply to a Classmate

Review a classmate’s population model scenario, equation, and algorithm. If no other classmate has yet responded, review their model for accuracy by providing an input value for n ≥ 5 and perform a trace of the algorithm.

Address the following:

Write out the outputs in a trace table.

Select two future population estimates (two output values of an) and discuss whether the output produced is appropriate for the scenario. What limitations, or problems, may there be in using this model to estimate the population indefinitely?

Based on your assessment of the output and potential limitations of the model, suggest a change to the general formula or algorithm for their sequence to represent a potentially better long-term model for the scenario. (You may consider the factors that were described in the initial planning phase or other biological limitations on growth/decline of populations.)

Post 3: Reply to Another Classmate

Review a different classmate’s population model scenario, equation, and algorithm. You will improve their model to account for a potential event that could affect the population growth/decline.

Modify your classmate’s population model by adjusting their algorithm with a conditional statement (if-then or if-then-else) for some event that leads the population to slow its growth or decline (or reverse between growth versus decline) at a specific population size (i.e., you choose a specific value of an).

Address the following:

Copy their original algorithm into your post and insert a conditional operation into an appropriate place to account for this change in the model. (You will need to incorporate a second formula with an updated value for d or r, for use when your conditional operation begins taking effect.)

Select an input value for n, large enough so that it will trigger your conditional statement to calculate some population estimates using your revised model, or second formula.

Perform a trace of the algorithm using this value of n and write out the outputs in a trace table.

Describe and explain the results, commenting specifically in your role as a consultant on how you believe this is now a good long-term modeling algorithm for the scenario.

2 Peer Posts have been provided in the attached Word Document. Following the Directions below, and following the examples, I need a response for each of these posts. There must be one of each type of response, as outlined in the instructions below. Post 2: Reply to a Classmate

Review a classmate’s population model scenario, equation, and algorithm. If no other classmate has yet responded, review their model for accuracy by providing an input value for n ≥ 5 and perform a trace of the algorithm.

Address the following:

Write out the outputs in a trace table.

Select two future population estimates (two output values of an) and discuss whether the output produced is appropriate for the scenario. What limitations, or problems, may there be in using this model to estimate the population indefinitely?

Based on your assessment of the output and potential limitations of the model, suggest a change to the general formula or algorithm for their sequence to represent a potentially better long-term model for the scenario. (You may consider the factors that were described in the initial planning phase or other biological limitations on growth/decline of populations.)

Post 3: Reply to Another Classmate

Review a different classmate’s population model scenario, equation, and algorithm. You will improve their model to account for a potential event that could affect the population growth/decline.

Modify your classmate’s population model by adjusting their algorithm with a conditional statement (if-then or if-then-else) for some event that leads the population to slow its growth or decline (or reverse between growth versus decline) at a specific population size (i.e., you choose a specific value of an).

Address the following:

Copy their original algorithm into your post and insert a conditional operation into an appropriate place to account for this change in the model. (You will need to incorporate a second formula with an updated value for d or r, for use when your conditional operation begins taking effect.)

Select an input value for n, large enough so that it will trigger your conditional statement to calculate some population estimates using your revised model, or second formula.

Perform a trace of the algorithm using this value of n and write out the outputs in a trace table.

Describe and explain the results, commenting specifically in your role as a consultant on how you believe this is now a good long-term modeling algorithm for the scenario.

Activity I – Last year, your firm collected data on each of its 107 division managers. The data contain growth figures for each manager’s division, the manager’s tenure with the firm, and the manager’s score on a leadership test, which was administered firmwide. These data are contained in the file attached.

Run a regression designed to determine the effect of manager tenure on division growth.

What role, if any, can the manager’s leadership test score play in the regression you ran for Part a? Explain.

Activity II – Use the data in the attached for this question.

You are working as an analyst for a large cable company that offers bundles of channels all across the United States. One of the bundles is the “basic package,” which includes network channels along with a few other basic cable channels. You are interested in learning how the price of this basic package influences the rate of subscriptions in a market. You have data on subscriptions per 1,000 local residents, price for the basic package, and average local household income. You also have data on local telecom labor costs per subscriber. You believe this last variable influences the local price but not subscriptions per se.

Based on the data provided, write out an expression for the data-generating process for subscriptions per 1,000 local residents.

Estimate the effect of basic package price on subscriptions per 1,000 local residents using OLS. Why might you distrust this result as being a causal effect?