Free Printable Set Theory

1.

For the given sets A and B, which statement is true?

a)

A ⊂ B

b)

B ⊂ A

c)

A = B

d)

A^'= B

2.

List the elements of B

a)

{4,5,6,7,8,9,10,11}

b)

{4,6,7,8}

c)

{9,5,10,11}

d)

{4,5,6,7,8,9,10}

3.

If A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 7}, what is A ∩ B?

a)

{3, 5, 7}

b)

{2, 3, 5, 7}

c)

{2, 3, 5, 7, 9}

d)

{1, 2, 3, 5, 7, 9}

4.

If A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 7}, what is A ∪ B?

a)

A ∪ B = {3, 5, 7}

b)

A ∪ B = {2, 3, 5, 7}

c)

A ∪ B = {2, 3, 5, 7, 9}

d)

A ∪ B = {1, 2, 3, 5, 7, 9}

5.

Find the cardinality of set A:

A = {14, 16, 18, 20, 22, 24}

a)

n(A) = 6

b)

n(A) = 12

c)

n(A) = 4

d)

n(A) = 8

6.

What does this symbol ( ∪ ) represent in set theory?

a)

Union

b)

Intersection

c)

Disjointed

d)

Subset

7.

What does this symbol ( ∩ ) represent in set theory?

a)

Union

b)

Intersection

c)

Disjointed

d)

Subset

8.

What type of set is denoted as either { } or ∅?

a)

Universal Set

b)

Empty (or Null) Set

c)

Disjointed Set

d)

Complement of a Set

9.

Let A = {2, 3, 4, 5, 6, 7} B = {2, 4, 7, 8) and C = {2, 4}.

Fill in the blanks by ⊂ or ⊄ to make the resulting statements true.

B __ A

a)

⊂

b)

⊄

10.

Let A = {2, 3, 4, 5, 6, 7} B = {2, 4, 7, 8) and C = {2, 4}.

Fill in the blanks by ⊂ or ⊄ to make the resulting statements true.

C __ A

a)

⊂

b)

⊄

11.

Determine if the statement is true or false.
{10, 12, 14, 16} ⊆ {1,2,3,4,...99}

a)

True

b)

False

12.

This is an example of ______________

$\left\{x\left|x\epsilon N\ and\ x\le5\right|\right\}$

a)

Roster Form

b)

Discriptive Form

c)

Set Builder Notation

13.

This is an example of ______________

{A, B, C, D, E, F, G, H, I, J, K, L, M}

a)

Roster Form

b)

Descriptive Form

c)

Set Builder Notation

14.

What does this symbol ( ⊆ ) represent in set theory?

a)

Union

b)

Intersection

c)

Disjointed

d)

Subset

15.

Which of the following sets is empty?

a)

A set with natural number divisible by 2

b)

A set containing a list of names of humans who traveled to the sun.

c)

A set containing the planets in the solar system

d)

A set of whole numbers smaller than 50

16.

{1,2,3,4,5,6} which set is a subset of this?

a)

{1,3,5}

b)

{0,1,2}

c)

{4,6,8}

d)

{1.1,2,3}

17.

{ three } and { t, h, r, e, e } are :

a)

Equal

b)

Equivalent

c)

Equal and Equivalent

d)

Neither

18.

A = {2, 4, 6, 8}

B = {8, 4, 6, 2}

Determine if these two sets are equal, equivalent, both or neither

a)

Equal

b)

Equivalent

c)

Both

d)

Neither

19.

Let A={1, 3, 4} and B={x|x is an even whole number less than 9}. Find A U B

a)

{1, 3, 4}

b)

{1, 2, 3, 4, 6, 8}

c)

{1, 2, 3, 4, 5, 6, 7, 8}

d)

{1, 2, 3, 4, 5, 6, 7}

20.

What does the shaded portion of the Venn diagram represent?

a)

Band and Art

b)

Only Art

c)

Band or Art

d)

Neither

21.

Identify the shaded area...

a)

A

b)

B

c)

A'

d)

B'

22.

Identify the shaded area...

a)

A

b)

B

c)

A'

d)

B'

23.

Identify the shaded area...

a)

A

b)

B

c)

A'

d)

B'

24.

Identify the shaded area...

a)

A∩B

b)

A∪B

c)

A'∩B'

d)

A'∪B'

25.

Identify the shaded area...

a)

A∩B

b)

A∪B

c)

A'∩B'

d)

A'∪B'

26.

Identify the shaded area...

a)

A∩B

b)

A∪B

c)

A'∩B'

d)

A'∪B'

27.

Identify the shaded area...

a)

A'∩B

b)

A∩B'

c)

A∪B'

d)

A'∪B

28.

What is a set?

a)

A method of solving problems

b)

A collection of objects

c)

A 2-D shape

d)

{7}

29.

Classify the following number: $\sqrt{2}$

a)

Real

b)

Rational

c)

Irrational

d)

Integer

30.

$0<n\le1$ Which number satisfies the following inequality?

a)

1.001

b)

$\sqrt{2}$

c)

0.2

d)

-1

31.

{1,2,3,4,5,6} which set is a subset of this?

a)

{1,3,5}

b)

{0,1,2}

c)

{4,6,8}

d)

{1.1,2,3}

32.

Find n(A) for the set:

A = {14, 16, 18, 20, 22, 24}

n(A) means cardinality (number of elements)

a)

6

b)

12

c)

4

d)

8

33.

The Universal Set = { -4, 3, -2, -1, 0, 1, 2, 3 ,4} and A = {0}.
What is the complement of A?

a)

{-4, -3, -2, -1, 0, 1, 2, 3}

b)

{-3, -2, -1, 1, 2, 3}

c)

{-4, -3, -2, -1, 1, 2, 3, 4}

d)

{-4, -3, -2, -1, 1, 2, 3}

34.

What statement does the shaded region represent?

a)

A or B and C

b)

Not C

c)

A or B

d)

B and C or A

35.

What statement does the shaded region represent?

a)

A ∩ B ∩ C

b)

A ∪ B ∩ C

c)

B ∩ C

d)

A ∪ C

36.

Let A = {3, 6, 9, 12, 15} and B = {4, 8, 12, 16}. Which of the following is true about the two sets?

a)

A\cup B=\left\{12\right\}

b)

$A\cap B=\left\{3,\ 4,\ 6,\ 8,\ 9,\ 12,\ 15,\ 16\right\}$

c)

$A-B=\left\{3,\ 6,\ 9,\ 15\right\}$

d)

$A-B=\left\{4,\ 8,\ 16\right\}$

37.

The set S = {fever, dry cough, tiredness} list the common symptoms of COVID-19. What is the cardinality of this set?

a)

3

b)

4

c)

5

d)

6

38.

What is the cardinality of $\phi$ ?

a)

0

b)

1

c)

Empty set

d)

None

39.

What is the cardinality of $\phi$ ?

a)

0

b)

1

c)

Empty set

d)

None

40.

If T = {different types of triangles} and Q = {different type of quadrilaterals}, then which of the following is the most suitable for Universal set?

a)

U = {x | x is a plane figure}

b)

U = { x | x is a shape}

c)

U = { x | x is a polygon}

d)

U = { x | x is a figure}

41.

Let K be the set of the letters in the sentence 'Keep safe'. How do you write this set correctly using the Roster Method?

a)

K = {k, e, e, p, s, a, f, e}

b)

K = {k, e, p, s, e, f}

c)

K = {k, e, e, p, s, a, f}

d)

K = {k, e, p, s, a, f}

42.

Which of the following cannot be considered a subset of H = {h, e, a, l, t, h, y}?

a)

W = {h, e, a, l, t, h, y}

b)

M = { }

c)

F = {h, e, a, t}

d)

R = {h, e, a, r, t}

43.

Which of the following is not an element of the set V = { 3x | x is a counting number from 3 to 9 }

a)

3

b)

9

c)

15

d)

21

44.

What is the cardinality of the set W = {0, 1, 2, 3,...100}?

a)

5

b)

6

c)

100

d)

101

45.

How many subsets does the set L = {l, o, v, e} have?

a)

4

b)

6

c)

8

d)

16

46.

Let O = {1, 3, 5, 7, 9, 11, 13, 15} and P = {1, 2, 3, 5, 7, 11, 13}. Find $O-P$ .

a)

$O-P=\left\{1,\ 2,\ 3,\ 5,\ 7,\ 9,\ 11,\ 13,\ 15\right\}$

b)

$O-P=\left\{1,\ 3,\ 5,\ 7,\ 11,\ 13\right\}$

c)

$O-P=\left\{9,\ 15\right\}$

d)

$O-P=\left\{2\right\}$

47.

Which of the following is a well-defined set?

a)

A set of delicious dishes.

b)

A set of world continents.

c)

A set of male president.

d)

A set of tall classmates.

48.

Which of the following describes the set M = {8, 16, 24, 32,40}

a)

A set of numbers between 8 to 40.

b)

A set of even numbers from 8 to 40.

c)

A set of numbers divisible by 8.

d)

A set of multiples of 8 from 8 to 40.

49.

The event _______ consists of all outcomes that are in both A

and B.

a)

A union B

b)

A intersection B

c)

A complement

d)

A difference B

50.

What is the meaning of disjoint in set theory?

a)

two or more sets having no elements in common

b)

two or more sets that do not match

c)

sets that are in different universal sets

d)

sets that contain no elements

51.

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.

52.

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)

2

b)

5

c)

1

d)

7

53.

Consider the following Venn diagram of herbivores and carnivores:

Determine H ∪ C

a)

{moose, rabbit, deer, squirrel}

b)

{bear, raccoon, badger}

c)

{cougar, wolf}

d)

{moose, rabbit, deer, squirrel, bear, raccoon, badger, cougar, wolf}

54.

From the above Venn diagram, what is the set (S ∪ T) ∩ V?

a)

{casey, drew, jade, glen}

b)

{alex, glen, hunter, jade}

c)

{casey, drew, glen}

d)

{drew, jade}

55.

Given:

U = { 1,2,3,r,t,h}, A = {3, r , t}, and T = U:

Find (T - A)'

a)

{1,2,h}

b)

A

c)

{1,2,3}

d)

U

56.

Let
U = {r, o, y, g, b, p}
C = {o, g, b}
W = {r, o, y, g}
N = {b, p}

Find

\left(C\cap W\right)'\cup N

a)

{r,y,b,p}

b)

{o,g,b,p}

c)

$\phi$

d)

U

57.

According to DeMorgan's Law: which of the following is equivalent to

A'\cup B'

a)

$\left(A\cup B\right)'$

b)

$\left(A\cap B\right)'$

c)

$A\cup B$

d)

$A'\cap B'$

58.

List the members in the following sets: B = { letters used in the word 'mathematics' }

a)

B = { m, a, t, h, e, m, a, t, i, c, s}

b)

B = { m, h, e, a, t, i, c, s}

c)

B = { m, a, t, h, e, a, t, i, c, s}

d)

B = {s, c, i, t, a, m, e, h, t, a, m}

59.

List the members in the following set: { even numbers less than 12 }

a)

{2, 6, 8, 10, 12}

b)

(2 4 6 8 10)

c)

{2, 4, 6, 8, 10}

d)

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

60.

Which of the following symbols represent "is a member of"

a)

$\infty$

b)

$\notin$

c)

$\subset$

d)

$\in$

61.

What is a finite set?

a)

All elements in the set are equal

b)

All elements in the set can be named and not counted

c)

All elements in the set can be counted and named

d)

All elements in the set has a set which can be counted.

62.

Let B = {a,b,c,d} and C = {d,c,b,a}. Sets B and C are ____ sets?

a)

Equal

b)

Equilateral

c)

Unequal

d)

Equivalent

63.

The Universal set is represented by:

a)

$\cap$

b)

$\exists$

c)

$\cup$

d)

$\subseteq$

64.

Equivalent sets have:

a)

The exact same elements

b)

The same number of subsets

c)

Nothing

d)

The opposite elements

65.

Let S = (2, 4, 6, 8, 10, 12, 14, 16}, calculate the number of subsets in S

a)

16

b)

512

c)

280

d)

256

66.

The notation n(B) means: ______________

a)

The number of elements in set B

b)

The number of sets in set B

c)

The number of elements outside set B

d)

The number of elements not included in set B

67.

If B and A are two sets, and all the elements in B is contained in A, then:

a)

$A\notin B$

b)

$B\ \subset\ A$

c)

$A\ \exists\ B$

d)

$A\ \cap\ B$

68.

Z = { Prime numbers less than 17} = { 1, 2, 3, 5, 7, 9, 11, 13, 15}

a)

True

b)

False

Set Theory

Total questions: 68

Worksheet time: 1hrs 13mins

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