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CHAPTER 1 Sets, Proof Templates, and Induction
rn Exercises
1. In a class of 35 students who are either biology majors or have blonde hair, there are
27 biology majors and 21 blondes. How many biology majors must be blonde?
2. A film class had 33 students who liked Hitchcock movies, 21 students who liked Spielberg movies, and 17 students who liked both kinds of films. How many students were
in the class if every student is represented in the survey?
3. A tennis camp has 39 players. There are 25 left-handed players and 22 players who
have a two-handed back stroke. How many left-handed players have a two-handed
back stroke if every player is represented in these two counts?
4. A car manufacturer determines that automatic transmission, power steering, and a
CD player are the three most important features in generating sales. The production
schedule for the next day has these features incorporated in cars as shown in the following table:
Car
Automatic Transmission Power Steering CD Player
A
x
x
B
x
x
x
C
x
D
x
x
E
x
F
x
x
G
x
x
H
x
x
(a) How many cars have at least one of these features? Even though you can see the
answer, use the Principle of Inclusion-Exclusion to derive it.
(b) How many cars have two or more of these features? Again, use the Principle of
Inclusion-Exclusion to derive the answer.
5. A marketing class did a survey of the number of fast-food outlets near campus. The
results of the survey showed the following:
Type of Food Sold
No. of Outlets
Hamburgers
15
Tacos
25
Pizza
21
Hamburgers and tacos
11
Hamburgers and pizza
10
Tacos and pizza
14
Hamburgers and tacos and pizza
9
Served none of these items
5