Basic Mathematics for College Students

A-26 Appendix III Inductive and Deductive Reasoning

WHYThe best way to examine this much information is to describe the situation

using a table.

Solution

The following table shows each course, with each possible instructor.

Since Professors A and B don’t want to teach calculus, we can cross them off

the calculus list. Since Professor C wants to teach statistics, we can cross her off

every other list. This leaves Professor D as the only person to teach calculus, so we

can cross her off every other list. Since Professor B wants to teach algebra, we can

cross him off every other list. Thus, the only remaining person left to teach

trigonometry is Professor A.

Calculus Algebra Statistics Trigonometry

AAA A

BBB B

CCC C

DDD D

Calculus Algebra Statistics Trigonometry

AA A

B

C

D D D D

C C C

B B B

A

EXAMPLE (^7) State Flags The graph
below gives the number of state flags that
feature an eagle, a star, or both. How many
state flags have neither an eagle nor a star?
StrategyWe will use two intersecting circles to model this situation.
WHYThe intersection is a way to represent the number of state flags that have
both an eagle and a star.
Solution
In figure (a) on the following page, the intersection (overlap) of the circles shows
that there are 5 state flags that have both an eagle and a star. If an eagle appears on
a total of 10 flags, then the red circle must contain 5 more flags outside of the
Has an eagle
Has a star
Has an eagle
and a star
10
27
5
Self Check 7
USED CARS Of the 50 cars on a
used-car lot, 9 are red, 31 are
foreign models, and 6 are red,
foreign models. If a customer
wants to buy an American model
that is not red, how many cars
does she have to choose from?
Now TryProblem 35