Name: 
 

Ch 3 Section 1 and 2 Formative Test



Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 

What is the meaning of complement in set theory?
A.
all the elements in the universal set that are not identical
B.
a set of elements that work well with a given set
C.
all the elements of a universal set that do not belong to a subset of it
D.
all the elements that are the opposite of the elements in a given set
 

 2. 

What is the universal set?
A.
a set with an infinite number of elements
B.
a set of all the elements under consideration for a particular context
C.
a set with a countable number of elements
D.
a set that contains every possible element
 

 3. 

Which statement is true?
A.
The English language and the French language are disjoint sets.
B.
Hockey equipment and lacrosse equipment are disjoint sets.
C.
Band instruments and orchestral instruments are disjoint sets.
D.
Linear equations and quadratic equations are disjoint sets.
 

 4. 

Which pair of sets represents disjoint sets?
A.
N, the set of natural numbers, and I, the set of integers
B.
T, the set of all triangles, and C, the set of all circles
C.
N, the set of natural numbers, and P, the set of positive integers
D.
none of the above
 

 5. 

Which pair of sets represents equal sets?
A.
N, the set of natural numbers, and I, the set of integers
B.
T, the set of all triangles, and C, the set of all circles
C.
N, the set of natural numbers, and P, the set of positive integers
D.
none of the above
 

 6. 

Which pair of sets represents one set being a subset of another but is not equal?
A.
N, the set of natural numbers, and I, the set of integers
B.
T, the set of all triangles, and C, the set of all circles
C.
N, the set of natural numbers, and P, the set of positive integers
D.
none of the above
 

 7. 

Rahim described the set as follows:
M = {all of the foods he eats}
D = {his favourite desserts}
V = {his favourite vegetables}
F = {his favourite fruits}

Assume Rahim likes some fruit for dessert. Which statement is true?
A.
The universal set is D, Rahim’s favourite desserts.
B.
Set F is a subset of D.
C.
Set D is a subset of V.
D.
Set M and set V are mutually exclusive.
 

 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 is the complement of P?
A.
the even numbers of U
B.
the universal set excluding the set of X
C.
the positive integers greater than 20
D.
the non-prime numbers of U
 

 9. 

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.
mc009-1.jpg
B.
mc009-2.jpg
C.
mc009-3.jpg
D.
mc009-4.jpg
 

 10. 

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 statement describes O¢?
A.
the set of even numbers of U
B.
the set of odd numbers of U
C.
the set of odd, prime numbers of U
D.
the set of even, prime numbers of U
 

Short Answer
 

 1. 

Tania recorded the 16 possible sums that can occur when you roll two four-sided dice.
S = {all possible sums}
• L = {all sums less than 4}
• G = {all sums greater than 4}
• F = {all sums equal to 4}
What is n(F)?
 

 2. 

Tania recorded the 16 possible sums that can occur when you roll two four-sided dice.
S = {all possible sums}
• L = {all sums less than 4}
• G = {all sums greater than 4}
• F = {all sums equal to 4}
What is the number of sums less than or greater than 4?
 

 3. 

Tania recorded the 16 possible sums that can occur when you roll two four-sided dice.
S = {all possible sums}
• L = {all sums less than 4}
• G = {all sums greater than 4}
• F = {all sums equal to 4}
Describes the relationship between the sets L and G.
 

 4. 

Tania recorded the 16 possible sums that can occur when you roll two four-sided dice.
S = {all possible sums}
• L = {all sums less than 4}
• G = {all sums greater than 4}
• F = {all sums equal to 4}
Describes the relationship between events L and G.
 

 5. 

Consider the following information.
• 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?
 

 6. 

Carlos surveyed 50 students about their favourite subjects in school. He recorded his results.
Favourite SubjectNumber of Students
mathematics
18
science
15
neither mathematics nor science
20

Determine how many students like only mathematics or only science.
 

 7. 

Mr. McSherry’s physics class is visiting the local amusement park. He has 33 students. Of these students, 21 plan to ride the roller coaster and 12 plan to ride the vertical drop. There are 7 students who do not plan to ride either attraction.

Determine how many students plan to ride only the roller coaster.
 

Problem
 

 1. 

a) Indicate the multiples of 2 and 3, from 1 to 100, using set notation. List any subsets.
b) Represent the sets and subsets in a Venn diagram.
 

 2. 

a) Indicate the multiples of 5 and 50, from 1 to 500, using set notation. List any subsets.
b) Represent the sets and subsets in a Venn diagram.
 

 3. 

a) List 10 of your favourite foods.
b) Organize this information into at least three sets.
c) Display the information in a Venn diagram.
 

 4. 

a) Draw a Venn diagram to represent these sets:
• the universal set U = {natural numbers from 1 to 50 inclusive}
T = {multiples of 3}
S = {multiples of 6}
N = {multiples of 19}
b) List the disjoints sets, if there are any.
c) Is each statement true or false? Explain.
i) T Ì S
ii) S Ì T
iii) N Ì N
iv) T¢ = {even numbers from 1 to 50}
v)
In this example, the set of natural numbers from 51 to 100 is { }.
 



 
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