Basic Mathematics for College Students

Appendix III Inductive and Deductive Reasoning A-27

intersection, as shown in figure (b). If a total of 27 flags have a star, the blue circle
must contain 22 more flags outside the intersection, as shown.

From figure (a), we see that 5  5 22, or 32 flags have an eagle, a star, or both.
To find how many flags have neither an eagle nor a star, we subtract this total from
the number of state flags, which is 50.

50  32  18

There are 18 state flags that have neither an eagle nor a star.

Eagle

5 flags have

both an eagle

and a star.

5 + 5 = 10

flags have

an eagle.

5 + 22 = 27

flags have

a star.

Star

(a)

Eagle Star

5 522

(b)

5

1. 5 2.0.9 3.M 4. 5. 7. 16

ANSWERS TO SELF CHECKS

Fill in the blanks.

1. reasoning draws general conclusions from
   specific observations.


2. reasoning moves from the general case to
   the specific.

Tell whether the pattern shown is increasing, decreasing,
alternating, or circular.

3. 2,3,4,2,3,4,2,3,4,...


4. 8, 5, 2,1,...


5. 2,4,2,0,6,...


6. 0.1, 0.5, 0.9, 1.3,...


7. a,c,b,d,c,e,...

8.

9. ROOM SCHEDULING From the chart, determine
   what time(s) on a Wednesday morning a practice room

,,,,

...

CONCEPTS

VOCABULARY in a music building is available. The symbol X indicates

that the room has already been reserved.

10. COUNSELING QUESTIONNAIRE A group of
    college students were asked whether they were taking
    a mathematics course and whether they were taking
    an English course. The results are displayed below.
    a. How many students were taking a mathematics
    course and an English course?
    b. How many students
    were taking an
    English course but
    not a mathematics
    course?
    c. How many students
    were taking a
    mathematics
    course?

Mathematics

class

English

class

10 11 18

APPENDIX III STUDY SET

MTWThF

9 A.M.X X X

10 A.M.XX X

11 a.m. X X X