120 CHAPTER 3
Log
Exercise Set 3.1
College
Students
Business
Majors
In Exercises 25-28, use the representations shown at the bottom
the previous column to express each symbolic statement in
What can you conclude about the resulting verbal statement
26.-9
27.-
wote
25. P
2.
equivalent way
In Exercises 57-56,
Express each
with "all," "son
b. Write the negar
51. Nobody doesn't ta
52. A problem well st
53. Nothing is both sa
54. Many a person ha
55. Not every great a
56. Not every genero
In Exercises 29-42,
a. Express the quantified statement in an
is, in a way that has exactly the same meaning
b. Write the negation of the quantified statement. (The ne te
should begin with "all," "some," or "no")
29. All whales are mammals.
30. All journalists are writers.
31. Some students are business majors.
32. Some movies are comedies.
33. Some thieves are not criminals.
34. Some pianists are not keyboard players.
35. No Democratic presidents have been impeached
36. No women have served as Supreme Court justices.
37. There are no seniors who did not graduate.
38. There are no applicants who were not hired.
39. Not all parrots are pets.
40. Not all dogs are playful.
41. All atheists are not churchgoers.
42. All burnt muffins are not edible.
Application Exerc
In Exercises 57 and 58
57. The City Council
citizens that in th
the city to its a
did not keep its
Therefore, durin
a. No major to
b. Atleast one
C.
Practice Exercises
In Exercises 1-14, determine whether or not cach sentence is a
statement
1. René Descartes came up with the theory of analytic geometry
by watching a fly walk across a ceiling,
2. The number of US patients killed annually by medical errors
is equivalent to four jumbo jets crashing each week.
3. On January 20, 2013, Mitt Romney became America's 45th
president
4. On January 20, 2009, Barack Obama became America's first
Hispanic president
5. Take the most interesting classes you can find.
6. Don't try to study on a Friday night in the dorms.
7. The average human brain contains 100 billion neurons.
8. There are 2.500,000 rivets in the Eiffel Tower.
9. Is the unexamined life worth living?
10. Is this the best of all possible worlds?
11. All US presidents with beards have been Republicans.
12. No U.S. president was an only child.
13. The shortest sentence in the English language is "Go!"
14. Go!
In Exercises 15-20, form the negation of each statement
15. It is raining.
16. It is snowing.
17. "Facts do not cease to exist because they are ignored."
-Aldous Huxley
18. "I'm not anti-social. I'm just not user friendly"
T-Shirt
(In this case, form the negation of both statements.)
19. It is not true that chocolate in moderation is good for the
heart
20. It is not true that Albert Einstein was offered the presidency
of Israel
In Exercises 21-24, let p, q, r, and s represent the following statements:
p: One works hard.
q: One succeeds
r: The temperature outside is not freezing.
s: It is not true that the heater is working.
Express each of the following statements symbolically
21. One does not work hard.
22. One does not succeed.
23. The temperature outside is freezing.
24. The heater is working.
According to Condensed Knowledge: A Deliciously Irreverent
Guide to Feeling Smart Again (Harper Collins, 2004), each
statement listed below is false.
p: Listening to classical music makes infants smarter.
q: Subliminal advertising makes you buy things
r Sigmund Freud's father was not 20 years older than his
mother
s Humans and bananas do nor share approximately 60% of
the same DNA structure
Here's another list of false statements from Condensed Knowledge
p. No Africans have Jewish ancestry.
q: No religious traditions recognize sexuality as central to
their understanding of the sacred.
r. All rap is hip-hop
s: Some hip-hop is not rap.
In Exercises 43-46, use the representations shown to express each
symbolic statement in words Verbal statements should begin wit
"all," "some," or "no. "What can you conclude about each result
verbal statement?
was not op
At least one
was open
d. The airport
58. During the Wa
Nixon assured
public service
indicated that
in his
years of
c.
43.-P
44.-9
45.-
46.5
a. Nixon alw
b. Nixon som
Nixon som
d. Nixon ney
Our culture celebra
for another person
graph illustrates th
important role in
Practice Plus
Exercises 47-50 contain diagrams that show relationships between
two sets. (These diagrams are just like the Venn diagrams studied
in Chapter 2. However, the circles are not enclosed in a rectangle
representing a universal set.)
Use each diagram to write a statement beginning with the
word "all," "some," or "no" that illustrates the relationship
between the sets
b. Determine if the statement in part (a) is true or false. If
false, write its negation.
Parrots
48.
Humans
60%
51%
50%
40%
47.
30%
Birds
20%
Mammals
10%
0
Pakistas
Source: Robert Lev
SOS
SECTION 3.1
Statements, Negations, and Quantified Statements
121
50.
49.
College
Students
Business
Majors
College
Students
Athletes
was shown at the bottom
bolie statement in word
18 verbal statement?
DO
00
28.
in an equivalent way, the
ame meaning
statement (The negation
"no")
In Exercises 51-56,
a. Express each statement in an equivalent way that begins
with "all," "some," or "no"
b. Write the negation of the statement in part (a).
51. Nobody doesn't like Sara Lee.
52. A problem well stated is a problem half solved.
53. Nothing is both safe and exciting.
54. Many a person has lived to regret a misspent youth.
55. Not every great actor is a Tom Hanks,
56. Not every generous philanthropist is a Bill Gates.
is.
Empeached
Durt justices.
rate.
hired.
c.
ndensed Knowledge
elity as central to
Application Exercises
In Exercises 57 and 58, choose the correct statement.
57. The City Council of a large northern metropolis promised its
citizens that in the event of snow, all major roads connecting
the city to its airport would remain open. The City Council
did not keep its promise during the first blizzard of the season.
Therefore, during the first blizzard:
a. No major roads connecting the city to the airport were open
b. At least one major road connecting the city to the airport
was not open
At least one major road connecting the city to the airport
was open
d. The airport was forced to close.
58. During the Watergate scandal in 1974, President Richard
Nixon assured the American people that "In all my years of
public service, I have never obstructed justice." Later, events
indicated that the president was not telling the truth. Therefore,
in bis years of public service:
a. Nixon always obstructed justice.
b. Nixon sometimes did not obstruct justice.
c. Nixon sometimes obstructed justice.
d. Nixon never obstructed justice.
Our culture celebrates romantic love-affection and sexual passion
for another person-as the basis for marriage. However, the bar
graph illustrates that in some countries, romantic love plays a less
important role in marriage.
Percentage of College Students willing
to Marry without Romantic Love
In Exercises 59-66, use the graph at the bottom of the previous
column to determine whether each statement is true or false. If the
statement is false, write its negation.
59. A majority of college students in Pakistan are willing to
marry without romantic love.
60. Nearly half of India's college students are willing to marry
without romantic love.
61. No college students in the United States are willing to marry
without romantic love.
62. All college students in Pakistan are willing to marry without
romantic love.
63. Not all college students in Mexico are willing to marry
without romantic love.
64. Not all college students in England are willing to marry
without romantic love.
65. The sentence "5% of college students in Australia are willing
to marry without romantic love" is not a statement.
66. The sentence "12% of college students in the Philippines are
willing to marry without romantic love" is not a statement.
Writing in Mathematics
67. What is a statement? Explain why commands, questions, and
opinions are not statements.
68. Explain how to form the negation of a given English
statement. Give an example.
69. Describe how the negation of statement p is
expressed using
symbols.
70. List the words identified as quantifiers. Give an example of a
statement that uses each of these quantifiers.
71. Explain how to write the negation of a quantified statement
in the form "All A are B." Give an example.
72. Explain how to write the negation of a quantified statement
in the form "Some A are B." Give an example.
73. If the ancient Greek god Zeus could do anything, could he create
a rock so huge that he could not move it? Explain your answer.
Critical Thinking Exercises
Make Sense? In Exercises 74–77, determine whether each statement
makes sense or does not make sense, and explain your reasoning.
74. I have no idea if a particular sentence is true or false, so I cannot
determine whether or not that sentence is a statement.
75. "All beagles are dogs" is true and "no beagles are dogs" is
false, so the second statement must be the negation of the
first statement.
76. Little Richard's "A-wop-bop-a-lula-a-wop-bam-boom!" is an
exclamation and not a statement.
77. Researchers at Cambridge University made the following
comments on how we read:
It deson't mtater waht oerdr the Itteres in a wrod are, so
Inog as the frist and Isat Itteer are in the crorcet pclae. Tihs is
bcuseae we dno't raed ervey Iteter but the wrod as a wlobe.
Because of the incorrect spellings in these sentences, neither
sentence is a statement.
78. Give an example of a sentence that is not a statement because
it is true and false simultaneously.
79. Give an example in which the statement "Some A are not B"
is true, but the statement "Some B are not A" is false.
80. "The statement
She isn't dating him because he is muscular
is confusing because it can mean two different things
Describe the two different meanings that make this statement
wwn to express each
should begin with
about each resulting
46. -
ationships between
diagrams studied
rectangle
used in a
60%
51%
49%
eginning with the
Es the relationship
50%
40%
ue or false
30%
20%
18%
10%
sals
10%
4%
Pakistan India Thailand Mexico England US.
mahir
Purchase answer to see full
attachment