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 visitors 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?

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