.jpg">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

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 listnotation. Your explanation may be a sentence that demonstrates your understand the notation.
1. (5 points) .gif">
Answer:
Explanation:
2. (5 points) Find .gif">, then determine which of these sets are equal?
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 andStarWars
II
8 students had seen
StarWars I andStarWars
III
10 students had
seen StarWars IIandStarWars
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 CTRLPRTSCRN 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
.jpg">
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 setbuilder 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

Explain your answer in this
column

n(C) =


n(P) =


n(V) =


n(C?P) =


n(C?V) =


n(V?P) =


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 wellstructured 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).