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The bar graph shows the percentage of Americans who were
not
100 happy, very happy, and pretty happy for four selected years
from 1980 through 2019. Use the information in the
graph to write
pach set in Exercises 133 - 138 in roster form or express the set as .
fer
rence
Level of Happiness in the United States
Not too happy
Very happy
Pretty happy
57
56
143. Describe the Venn diagram for two disjoint sets. How
does this diagram illustrate that the sets have no common
elements?
144. Describe the Venn diagram for proper subsets. How does
this diagram illustrate that the elements of one set are also
in the second set?
145. Describe the Venn diagram for two equal sets. How does
this diagram illustrate that the sets are equal?
146. Describe the Venn diagram for two sets with common
elements. How does the diagram illustrate this relationship?
147. Describe what is meant by the complement of a set.
148. Is it possible to find a set's complement if a universal set is
not given? Explain your answer.
149. Describe what is meant by the intersection of two sets. Give
an example.
150. Describe what is meant by the union of two sets. Give an
example.
151. Describe how to find the cardinal number of the union of
two finite sets.
60%
53
57
50%
40%
35
36
34
Percentage of Americans
30%
29
yer
20%
12
14
10%
10
the
1980
1990 2000
2010
Source: General Social Survey by the National Opinion Research Center
ካ
133. {x|x was a year in which more than 34% were very happy} n
{x|x was a year in which fewer than 14% were not too happy}
134. {x|x was a year in which more than 30% were very happy} n
{x|x was a year in which fewer than 12% were not too happy}
135. {x|x was a year in which more than 34% were very happy} U
{x|x was a year in which fewer than 14% were not too happy}
136. {x|x was a year in which more than 30% were very happy} U
{x|x was a year in which fewer than 12% were not too happy}
137. The set of years in which more than 55% were pretty happy
and 12% were not too happy
138. The set of years in which more than 55% were pretty happy
or 12% were not too happy
139. A winter resort took a poll of its 350 visitors to see which
winter activities people enjoyed. The results were as follows:
178 people liked to ski, 154 people liked to snowboard, and
49 people liked to ski and snowboard. How many people in
the poll liked to ski or snowboard?
140. A pet store surveyed 200 pet owners and obtained the
following results: 96 people owned cats, 97 people owned
dogs, and 29 people owned cats and dogs. How many people
in the survey owned cats or dogs?
Critical Thinking Exercises
Make Sense? In Exercises 152-155, determine whether each
statement makes sense or does not make sense, and explain your
reasoning
152. Set A and set B share only one element, so I don't need to
use overlapping circles to visualize their relationship.
153. Even if I'm not sure how mathematicians define irrational
and complex numbers, telling me how these sets are
related, I can construct a Venn diagram illustrating their
relationship
154. If I am given sets A and B, the set (AUB)' indicates
I should take the union of the complement of A and the
complement of B.
155. I suspect that at least 90% of college students have no
preference whether their professor is a man or a woman, so
I should place college professors in region IV of the Venn
diagram that precedes Exercises 117-122.
In Exercises 156-163, determine whether each statement is true
or false. If the statement is false, make the necessary change(s) to
produce a true statement.
156. n(AUB) = n(A) + n(B)
157. An A' = Ø
158. (AUB) CA
159. If A CB, then AnB = B.
160. ANU = U
161. A UZ = 8
162. If A CB, then AnB = Ø.
163. If B C A, then AnB = B.
Writing in Mathematics
141. Describe what is meant by a universal set. Provide an
example.
142. What is a Venn diagram and how is it used?
In xercises 164-167, assume A + B. Draw a Venn diagram tha
correctly illustrates the relationship between the sets.
164. AnB = A
165. AnB = B
166. AUB= A
167. AUB = B
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