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# 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....

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.

b. (1 point) How many students have seen exactly 2 of the movies?
c. (1 point) How many students have seen NONE of the movies? Explain how you got your answer.
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.

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?

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:

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?

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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