Foundations 30
Chapter 3 Review – Set Theory and Logic
Name:_______________________________ Date:________________________ Mark:_____/_____=_____%
Multiple Choice - Identify the choice that best completes the statement or answers the question. (25
Marks)
____
1. What is the meaning of complement in set theory?
A.
B.
C.
D.
____
2. What is the meaning of disjoint in set theory?
A.
B.
C.
D.
____
a set with an infinite number of elements
a set of all the elements under consideration for a particular context
a set with a countable number of elements
a set that contains every possible element
4. Which statement is false?
A.
B.
C.
D.
____
two or more sets having no elements in common
two or more sets that do not match
sets that are in different universal sets
sets that contain no elements
3. What is the universal set?
A.
B.
C.
D.
____
all the elements in the universal set that are not identical
a set of elements that work well with a given set
all the elements of a universal set that do not belong to a subset of it
all the elements that are the opposite of the elements in a given set
Trigonometry is a subset of mathematics.
The cities in Manitoba are a subset of the cities in Canada.
Squashes are a subset of vegetables.
Birds are a subset of mammals.
5. Which pair of sets represents disjoint sets?
A.
B.
C.
D.
N, the set of natural numbers, and I, the set of integers
T, the set of all triangles, and C, the set of all circles
N, the set of natural numbers, and P, the set of positive integers
none of the above
____
6. Given the following situation:
• the universal set U = {positive integers less than 20}
• X = {4, 5, 6, 7, 8}
• P = {prime numbers of U}
• O = {odd numbers of U}
Which set represents the odd, prime numbers of set U?
A.
B.
C.
D.
____
{0, 3, 5, 7, 11, 13, 17, 19}
{3, 5, 7, 11, 13, 17, 19}
{2, 3, 5, 7, 11, 13, 17, 19}
{1, 2, 3, 5, 7, 11, 13, 17, 19}
7. Given the following situation:
• the universal set U = {positive integers less than 20}
• X = {4, 5, 6, 7, 8}
• P = {prime numbers of U}
• O = {odd numbers of U}
Which is the complement of P?
A.
B.
C.
D.
the even numbers of U
the universal set excluding the set of X
the positive integers greater than 20
the non-prime numbers of U
____
8. Given the following situation:
• the universal set U = {positive integers less than 20}
• X = {4, 5, 6, 7, 8}
• P = {prime numbers of U}
• O = {odd numbers of U}
Which diagram represents the situation?
A.
B.
C.
D.
____
9. There are 28 students in Mr. Connelly’s Grade 12 mathematics class.
The number of students in the yearbook club and the number of students on student
council are shown in the Venn diagram. Use the diagram to answer the following
questions.
How many students are in both the yearbook club and on the student council?
A.
B.
C.
D.
2
5
1
7
____ 10. There are 28 students in Mr. Connelly’s Grade 12 mathematics class.
The number of students in the yearbook club and the number of students on student
council are shown in the Venn diagram. Use the diagram to answer the following
questions.
How many students are in the yearbook club but not on student council?
A.
B.
C.
D.
2
5
1
7
____ 11. There are 28 students in Mr. Connelly’s Grade 12 mathematics class.
The number of students in the yearbook club and the number of students on student
council are shown in the Venn diagram. Use the diagram to answer the following
questions.
How many students are in at least one of the yearbook club or on student council?
A.
B.
C.
D.
2
5
8
7
____ 12. Consider the following Venn diagram of herbivores and carnivores:
Determine H  C.
A.
B.
C.
D.
{moose, rabbit, deer, squirrel}
{bear, raccoon, badger}
{cougar, wolf}
{moose, rabbit, deer, squirrel, bear, raccoon, badger, cougar, wolf}
____ 13. Consider the following Venn diagram of herbivores and carnivores:
Determine n(H  C).
A.
B.
C.
D.
2
9
4
3
____ 14. Consider the following Venn diagram of herbivores and carnivores:
Determine H  C.
A.
B.
C.
D.
{moose, rabbit, deer, squirrel}
{bear, raccoon, badger}
{cougar, wolf}
{moose, rabbit, deer, squirrel, bear, raccoon, badger, cougar, wolf}
____ 15. Consider the following two sets:
• A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
• B = {–9, –6, –3, 0, 3, 6, 9, 12}
Which Venn diagram correctly represents these two sets?
A.
B.
C.
D.
____ 16. A summer camp offers canoeing, rock climbing, and archery. The following Venn diagram
shows the types of activities the campers like.
Use the diagram to determine n((R  C) \ A).
A.
B.
C.
D.
64
48
37
59
____ 17. A summer camp offers canoeing, rock climbing, and archery. The following Venn diagram
shows the types of activities the campers like.
Use the diagram to determine n((R  A) \ C).
A.
B.
C.
D.
14
5
26
8
____ 18. A summer camp offers canoeing, rock climbing, and archery. The following Venn diagram
shows the types of activities the campers like.
Use the diagram to determine n((A  C)  (R  A)).
A.
B.
C.
D.
16
27
5
11
____ 19. What is a hypothesis?
A.
B.
C.
D.
an idea
a statement
a clue
an assumption
____ 20. What is a conclusion?
A.
B.
C.
D.
the result of a hypothesis
an assumption
a decision
the answer to a statement
____ 21. Which sentence is written as a conditional statement?
A.
B.
C.
D.
You can fool some of the people some of the time but you can’t fool me.
If you are a farmer, then you live in the country.
If you can’t beat them, join them.
You get wet if you stand in the rain.
____ 22. Which sentence is the converse to the conditional statement below?
“If the milk is not refrigerated, then it will spoil.”
A.
B.
C.
D.
Unrefrigerated milk will spoil.
The milk is spoiled because it was not put in the refrigerator.
If the milk is spoiled, then it is not refrigerated.
The milk will spoil if it is not put in the refrigerator.
____ 23. Which conditional statement is biconditional?
A.
B.
C.
D.
If you live in PEI, then you live in the smallest province.
If you bought a condominium, then you own your home.
If you live in Kelowna, then you live in British Columbia.
If you live in a house, then you have a backyard.
____ 24. Which statement is the converse of the conditional statement below?
“If tomorrow is Monday, then today is Sunday.”
A.
B.
C.
D.
If tomorrow is Sunday, then today is not Monday.
If today is Sunday, then tomorrow is Monday.
If tomorrow is not Monday, then today is not Sunday.
If today is not Sunday, then tomorrow is not Monday.
____ 25. Which statement is the converse of the conditional statement below?
“If a bird has wings, then the bird can fly.”
A.
B.
C.
D.
If a bird does not have wings, then the bird cannot fly.
If the bird cannot fly, then the bird does not have wings.
If a bird can fly, then the bird has wings.
If a bird does not have wings, then the bird can fly.
Short Answer. Show your work whenever possible.
1. What is the set notation for the set of all natural numbers greater than 1 and less than or
equal to 50? (1 Mark)
2. Draw a Venn diagram to represent these sets. (4 Marks)
• the universal set U = {all grade 12 courses}
• S = {all social studies courses}
• H = {all history courses}
• G = {all geography courses}
• M = {all mathematics courses}
3. Consider the following information. (1 Mark)
• the universal set U = {all grade 12 courses}
• S = {all social studies courses}
• H = {all history courses}
• G = {all geography courses}
• M = {all mathematics courses}
What is the complement to set S?
4. Carlos surveyed 50 students about their favourite subjects in school. He recorded his
results.
Favourite Subject
mathematics
science
neither mathematics nor
science
Number of
Students
18
15
20
Determine how many students like both mathematics and science. (3 Marks)
5. A music school offers lessons on 8 different instruments.
piano
recorder
violin
steel drum
bagpipe
harmonica
xylophone
banjo
Determine the number of instruments with neither keys nor strings, (K  S)´. (1 Mark)
6. A men’s magazine surveyed 600 readers about their facial hair.
• 85 had a moustache
• 49 had a beard
• 483 were clean shaven
How many men had a beard and a moustache? (3 Marks)
7. The city surveyed 3000 people about how they travel to work.
• 1978 took public transit (P)
• 1494 drove (D)
• 818 cycled (C)
• 731 took public transit and drove only
• 298 took public transit and cycled only
• 27 drove and cycled only
• 164 used all three modes of transportation
How many people use public transit only? Use a Venn diagram to show your answer.
You must complete the whole Venn diagram to receive full marks. (9 Marks)
8. Write the converse of the conditional statement below. “If an animal is a polar bear, then
the animal has white fur.” (1 Mark)
9. If the statement below is biconditional, rewrite it in biconditional form. If the statement is
not biconditional, provide a counterexample. “If you have insomnia, then you cannot
sleep at night.” (2 Marks)
10. If the statement is biconditional rewrite it in biconditional form. If the statement is not
biconditional provide a counterexample. “If you are in the capital city of Canada, then you
are in Ottawa.” (2 Marks)
11. Show the biconditional statement below is true. If it is not true, give a counterexample.
“This month is August if and only if last month was July.” (2 Marks)
12. Verify the conditional statement below or disprove it with a counterexample. “If Mother’s
Day is this month, then it is May.” (2 Marks)
13. a) Verify the conditional statement below or disprove it with a counterexample. “If an
animal has four legs, then the animal is a cow.” (2 Marks)
b) Write the inverse of the above conditional statement. Verify the inverse or disprove it
with a counter example. (2 Marks)
c) Write the contrapositive of the above conditional statement. Verify the contrapositive or
disprove it with a counter example. (2 Marks)