IS 203
Exercise Set 8
Exercise Sets should be completed through group work, but each student will submit their own solutions. The following problems must be submitted through the assignment page in Canvas by 11:59 pm on Sunday, October 21, 2024.
Exercise sets are distributed as Word files so students have an easier time using the assignment. To properly see some symbols, the document must be opened in Word. Students who prefer to print out the exercise set and write their answers (or write answers on a tablet directly onto a document or pdf) should first insert extra lines between questions and problems.
Items highlighted yellow must be complete before class on Monday.
Items highlighted blue must be complete before class on Wednesday.
Items highlighted pink must be complete before class on Friday.
Items with no highlighting are suggestions of when to complete work in order to complete the exercise set on time.
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Problems to Submit
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When to Complete
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Part 1
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Monday
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Part 2
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Tuesday
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Part 3
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2, 4, & 5
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Wednesday & Thursday
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Part 4
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Thursday
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Part 5
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Set A, problem 2
Set B, problems 1 & 2
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Friday
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Comprehension Assessment
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Monday-Sunday
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Part 1: Indigenous Peoples’ Day
→Task: Watch documentary. You must be logged into your UIUC library account to access.
Part 2: Graph Theory 2
→Task: Watch Lecture Video 29.
Part 3: Paths and Circuits
1. List all paths that begin with vertex a.
2. List all circuits that begin with vertex d. Only use a loop once for each circuit.
3. Are each of the following graphs strongly connected, weakly connected, or not connected? Why or why not?
a.
b.
c.
4. Does the social network you created on Wednesday have an Euler Circuit or an Euler Path? Why or why not?
5. Does the social network you created on Wednesday have a Hamilton Circuit or a Hamilton Path? Why or why not?
Part 4: Dependent and Independent Probabilities
→ Task: Skim chapters 13.1 through 13.4 of the Statistics text and watch lecture video 30.
It is necessary to read the below instructions for use of the text. These instructions will apply to every set of exercises from this text throughout the semester.
Instructions for using Statistics text:
· The Statistics text is structured so that the problems in the text directly reference the material in the section they appear. It is not possible to accurately complete the problems without reading the text.
· Solutions for exercise sets denoted with letters (A, B, C, etc.) are at the back of the text.
· Solutions for Review Exercises at the back of a chapter do not have solutions provided.
· Work on exercise sets in the text until you are comfortable with the processes the problems cover. Some people will find they need to complete only a few problems and some people will find they need to complete many problems.
Part 5: Calculating Dependent and Independent Probabilities
Exercises from Chapter 13 of the Freedman text.
Exercise Set A (p 225)
Exercise Set B (p 227)
Comprehension Assessment on next page.
Comprehension Assessment 4
The comprehension assessment is due at the same time as the exercise set and can be submitted with the exercise set as a single document.
Total Grade Value: 100 points
Grading:
· All proofs must be written using the forms learned in class.
· No more than 50% of a point value for a part will be deducted no matter how many errors.
· 0% of the point value for a question, problem or section will be awarded if no work is shown or if a response is not attempted.
· Detailed rubrics for each part are included on the Canvas page for the Comprehension Assessment.
Part 1: 20 points
Use the following functions to determine if the requested composed function is one-to-one for ℤ. Reminder: all work must be shown to receive credit.
Hint: This is a more complex function than you have used before. It will be necessary to substitute multiple negative and positive values for x to determine if the function is one-to-one.
f (x) = 2 – (1/2)x g (x) = 2x
1. g (f (x))
Part 2: 20 points
2. Find a, d, and an for sn {2, 0, -2, -4, -6}
3. Find a, r, and an for sn {3, 2, 1 1/3, 8/9, 16/27}
Part 3: 30 points
Use the below sets for problems in Part 3.
A = {1, 2, 3} B = {1, 2}
For each problem, give the following:
o R
o The digraph of R.
o An explanation of why R is or is not reflexive.
o An explanation of why R is or is not symmetric.
o An explanation of why R is or is not transitive.
4. aRa: A x A → (a1, a2) ϵ R
5. aRb: a is a multiple of b → (a, b) ϵ R
Part 4: 10 points
Why did Dennis Banks lead a protest in Custer, South Dakota?
Part 5: 20 points
Note: all vertices are on the outer rim of the graph and are colored red. There is no vertex in the middle of the graph.
6. Does the above graph have an Euler Circuit? Why or why not?
7. Is it possible to determine if the graph has a Hamiltonian Circuit using a simple rule like you would for an Euler Circuit? Why or why not?
Extra Credit: (2 points if attempted, 4 points if correct)
Why is the American Indian Movement (AIM) an important organization to consider on Indigenous Peoples’ Day?