Unit 4: Sets – Assignment

Total points for Assignment: 35 points.

Assignments must be submitted as a Microsoft Word document and uploaded to the Dropbox for Unit 4.

All Assignments are due by Tuesday at 11:59 PM ET of the assigned Unit.

NOTE: Assignment problems should not be posted to the Discussion threads. Questions on the Assignment problems should be addressed to the instructor by sending an email or by attending office hours.

You must show your work on all problems. If a problem is worth 2 points and you only show the answer, then you will receive only 1 point credit. If you use a calculator or online website, give the

source and tell me exactly what you provided as input. For example, if you used Excel to compute 16 * 16, state “I typed =16*16 into Excel and got 256. You may type your answer right into this document.

Part I. Basic Computations

Questions 1 and 2 are based on the following information regarding this group of students.

Student

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Name

Gender

Hair Color

How many pairs of shoes do you own?

A

John

M

Black

3

B

Mary

F

Blonde

12

C

Kerry

F

Brown

8

D

Michael

M

Brown

1

E

Nakita

F

Red

34

F

Jill

F

Blonde

8

G

David

M

Brown

9

H

Eric

M

Black

2

A = { all male students}

B = {all students with brown hair}

C = {all students with more than 8 pairs of shoes}

Using the table above, determine the contents of the following sets and express them in list-notation.

Your explanation may be a sentence that demonstrates your understand the notation.

1. (5 points)

A′ ∪ B

Answer:

Explanation:

2.

(5 points) Find A ∪ ( B ∩ C ),

which of these sets are equal?

( A ∪ B) ∩ C ,

and ( A ∪ B ) ∩ ( A ∪ C ) , then determine

Answer:

Explanation:

3.

A group of students was surveyed for whether they had ever seen the first three sequels of

Star Wars. There were a total of 46 students in the group.

17 students had seen StarWars I

17 students had seen StarWars II

23 students had seen StarWars III

6 students had seen StarWars I and StarWars II

8 students had seen StarWars I and StarWars III

10 students had seen StarWars II and StarWars III

2 students had seen all three movies.

a. (3 points) Draw a Venn Diagram representing the students who have seen the three movies.

[In Microsoft Word 2007, you may use Insert/SmartArt to draw a Venn Diagram. Another

alternative is to use Creately.com to draw your diagram, then use CTRL-PRTSCRN to paste it into

this document. You may also draw the diagram by hand, take a picture of the drawing or scan it

in, then paste it into your document.] Explain the logical steps involved in arriving at the values for

each area of the diagram.

Answer:

Explanation:

b. (1 point) How many students have seen exactly 2 of the movies?

Answer:

Explanation:

c. (1 point) How many students have seen NONE of the movies ? Explain how you got your

answer.

Answer:

Explanation:

Part II. Case Study

The case of the Stolen Chemistry Exam

This week Patty Madeye is going to be investigating the theft

of a final exam for Chemistry 101 at a local university. At this

university, some students are considered resident students

(meaning that they live on campus) and some are considered

commuter students (they live elsewhere).

Patty learns that there are 150 students taking Chemistry 101

this semester. She considers every one of them a suspect in

the theft of the exam, since they are the only ones who could

benefit from seeing the exam. Since Patty has taken

Discrete Mathematics, she uses P to represent the set of

suspects.

P = {Set of all students taking Chemistry 101}

Task #1 (4 points) – In the first scene of the episode, Patty will find the envelope in which the exams

had been placed. The discarded envelope is in the garbage can near the student lounge frequented

by commuter students, which seems to indicate that whoever took the exam is a commuter student.

Using the forms of set notation that you learned about in this unit your first task is to express this set

of suspect students, which we will call C. Be sure to specify both the set-builder notation and the

descriptive notation.

Answer:

Explanation:

Task #2 (4 points) – Patty learns that there are 300 students are commuter students, 10 of which are

taking Chemistry 101. She needs some help representing these 10 students using the sets from

above.

How would you represent the set containing {all commuter students who are taking Chemistry 101}

using a set operation on C and P?

Answer:

Explanation:

Task #3 (4 points) – Further research from the security video tapes for the building where the exams

were stolen indicates that there were 86 people who entered the building around the time of the theft.

Of these 86 people (which we will identify as set V), 16 visited the commuter student lounge and 20 of

them were identified by the professor as being in the Chemistry 101 class. 51 of the vistors are

neither commuters nor students in the Chemistry class. Patty needs you to summarize all these

clues, as follows:

Complete this column with your

answer

n(C) =

n(P) =

n(V) =

n(C ∩ P) =

n(C ∩ V) =

n(V ∩ P) =

Explain your answer in this column

n(C U P) =

n((C U P)’ U V) =

Task #4 (8 points) – Patty looks at all these clues and does some quick figuring and says “I’ve got it!

I know who stole the exams!”. She asks you to draw a Venn Diagram, then write an explanation of

how you arrived at the numbers in the diagram. How does Patty know who stole the exams?

Answer:

Explanation:

Requirements

– This question does not require a long essay, however you must clearly state your answer in a

well-structured paragraphs using proper grammar, spelling, and sentence structure.

– This is not an “opinion” question – you must offer evidence from the data or your knowledge of set

theory.

– Don’t forget to explain how the problem can be solved with set theory. (Remember, the script

writers haven’t taken this class yet).

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