Discrete Mathematics for Computer Science

42 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 Spiel-
   berg 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 fol-
   lowing 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