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Worksheets

Notes on Sets

Total questions: 116

Worksheet time: 6hrs 22mins

Name
Class
Date
1.

List all the elements in A= {letters in the word "BOOK"}.

a)

A= {B,O,K}

b)

A= {B,O,O,K}

c)

A= {B,K}

d)
2.

Which symbol completes the statement correctly? {6}____{1,3,6}

a)

ϵ\epsilon

b)

\subset

c)

==

d)

⊄\not\subset

3.

Complete the statement correctly: Cow____ the set of all farm animals.

a)

ϵ\epsilon

b)

\subset

c)

\subseteq

d)

⊄\not\subset

4.

Which of the following is a well-defined set?

a)

{a happy child}

b)

{a popular TV series}

c)

{a favorite book by my classmates}

d)

{a Mathematics book in the school library}

5.

Which of these sets is equal to {L,O,V,E}?

a)

{O,V,E}

b)

{S,E,V,O,L}

c)

{O,E,L,V}

d)

{L,E,V}

6.

Which of these sets is equivalent but not equal to {Ram, Jay, Mick}

a)

{Mick, Jay, Olga}

b)

{Jay, Mick, Ram}

c)

{Mick, Jay, Ram}

d)

{Andy, Ram, Ed, Jay}

7.

Describe this set in words: {2,3,5,7,11,13,17,19}

a)

Set of prime numbers from 2 to 19

b)

Set of prime numbers less than 19

c)

Set of odd numbers less than 20

d)

Set of whole numbers less than 20

8.

Which of the following statements is TRUE?

a)

2 ϵ\epsilon {1,3,5,7}

b)

{5} ϵ\epsilon {5,10,15,20,}

c)

6 ϵ\epsilon {x/x is an odd number}

d)

3 ϵ\epsilon {x/x is a prime number}

9.

Consider M={vowels in the word "MATHEMATICS"}. Find n(M).

a)

4

b)

3

c)

7

d)

10

10.

Write {even whole numbers between 3 to 15} using the roster method.

a)

{3,5,7,9,11,13,15}

b)

{5,7,9,11,13}

c)

{4,6,8,10,12,14}

d)

{2,4,6,8,10,12,14,16}

11.

(a)   is a collection of well-defined objects.

12.

Another term for member of a set.

a)

element

b)

set

c)

set notation

d)

roster method

13.

"The set of honest people" is a _____set.

a)

well-defined

b)

not well-defined

14.

Which of the following is a well-defined set?

a)

The set of beautiful flowers

b)

The set of nice cars

c)

The set of good students

d)

The set of books in a shelf

15.

Which of these is an empty set?

a)

The set of green apples.

b)

The set of two-legged elephants

c)

The set of white shirts

d)

The set of green bananas

16.

What is the cardinality of set A is a counting number less than 10?

a)

7

b)

8

c)

9

d)

10

17.

Which of the following sets is infinite?

a)

Set W is a counting number less than 5.

b)

Set A is a set of whole number between 10 and 15.

c)

Set Y is a set of letters in the English alphabet after U.

d)

Set S is a set or prime numbers.

18.

Which of the following is true?

a)

The cardinality of an empty set is 1.

b)

If two sets have exactly the same elements, then they are equal.

c)

If two sets are equal, then they are equivalent.

d)

If two sets are equivalent, then they are equal.

19.

If two sets have exactly the same elements, then they are (a)   .

20.

If A = {a, b, c, d}, how many subsets does A have?

(a)  

21.

Which is not an infinite set?

a)

{x|x is a counting number greater than 15}

b)

{2, 4, 6,..}

c)

{x|x is a factor of 36}

d)

{x|x is a multiple of 9}

22.

Which set has denumerable elements?

a)

Universal Set

b)

Empty Set

c)

Infinite Set

d)

Finite Set

23.

What way of expressing sets lists down all the elements contained in the set?

a)

set-builder

b)

roster

c)

graphical

d)

semantic

24.

What operation on sets combine all the elements found in the sets selected?

a)

Union

b)

Intersection

c)

Complement

d)

Cardinality

25.

An instructive way of describing the relationships between sets and elements and are made up of circles which represent the sets.

a)

Venn Diaphragm

b)

Venn Diagram

c)

Venn Euler

d)

Venn Operations

26.
Set  Q  contains the letters in the word  SISTER .
 Which of the following is set  Q ?
a)
Q = { S, T, R }
b)
Q = { I, E }
c)
Q = { S, I, S, T, E, R }
d)
Q = { S, I, T, E, R }
27.

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

a)

Superset

b)

Disjointed Set

c)

Empty (or Null) Set

d)

Subset

28.

If A= {10,20,30,40},B={20,40,60} and C = {10,20,40,60,80}, find A Ո B Ո C

a)

{20,40}

b)

{20,40,60}

c)

{10,20,30,40,50,60,80}

d)

{10,20,30,...}

29.

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

a)

A ⊂ B

b)

B ⊂ A

c)

A = B

d)

A' = B

30.

Use the Venn diagram to identify the statement that is true.

a)

2 ∈ P ∩ Q

b)

5 ∈ Q

c)

{5,7} ⊆ P

d)

P U Q = Q

31.

List the elements of (A U B)'

a)

{1,4}

b)

{2,3,5,6,7,8,9}

c)

{2,3,6,7,8}

d)

{5,9}

32.

{ x | x is a Marymount Student}

a)

Roster Form

b)

Universal Form

c)

Set Builder Notation

d)

Equivalent Inequality

33.

Which of the following statements are true for the Venn diagram shown?

a)

Overlapping sets

b)

Subsets

c)

Disjoint sets

d)

Equal sets

34.

Which of the following statements are true for the Venn diagram shown?

a)

A is a subset of B

b)

B is a subset of A

c)

A = B

d)

A and B are disjoint sets

e)

B is a superset of A

35.

Determine if the following sets are:

a)

Subsets

b)

Equal sets

c)

Overlapping sets

d)

Disjoint sets

36.

How many subsets will this set have? A= {a, b, c} ?

a)

8

b)

6

c)

3

d)

0

37.
If every element in set A is also in set B, then...
a)
A is a subset of B
b)
B is a subset of A
c)
A = B
d)
A and B are disjoint
38.

Every set has _____ as one of its subsets (select all that apply.)

a)

b)

0

c)

itself

d)

the real numbers

39.

A = {x : x is a letter in the word SEAT}

B = {x : x is a letter in the word TASTE}


Determine if these two sets are equal or equivalent.

a)

Not equal because seat has 4 letters and taste has 5 letters.

b)

Equivalent because they have the same letters

c)

Equal because each set has the same cardinality and the same letters.

40.

Consider M={vowels in the word "MATHEMATICS"}. Find n(M).

a)

4

b)

3

c)

7

d)

10

41.

Set D is the set of the distinct letters in the word mathematics. Write the set using the Roster method.

a)

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

b)

D = {m, a, t, h}

c)

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

d)

D = {m, a, t, h, i, c, s}

42.

What is the cardinality of the set A = {whole numbers less than or equal to 20}?

a)

20

b)

21

c)

19

d)

18

43.

Which is a subset of X={1, 2}?

a)

{ }

b)

{1}

c)

{1,2}

d)

{2}

e)

all of the above

44.
Given that
R = { factors of  36 }. 
n(R) = 
a)
6
b)
9
c)
12
d)
15
45.
Given that
set  V = { m, n, o, p },
find the number of subsets  V.
a)
16
b)
12
c)
10
d)
8
46.

Which of the following is not a well-defined set?

a)

The set of boys in your class

b)

The set of even numbers

c)

The set of students wearing red dress

d)

The set of the colors of the rainbow

47.

The Universal set U= {the days of the week}, subset A= {Monday, Friday} what is A'?

a)

A' = {Monday, Friday}

b)

A'= {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}

c)

A'={Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}

48.

The group of intelligent students in a class is

a)

A finite set

b)

A null set

c)

A singleton set

d)

Not a well defined collection

49.

The group of intelligent students in a class is

a)

A finite set

b)

A null set

c)

A singleton set

d)

Not a well defined collection

50.

Let A = {2, 3, 4, 5, 6, 7}

B = {2, 4, 7, 8)

C = {2, 4}.

Which of the following mathematical statements is true?

a)

B ⊂ C

b)

A ⊂ C

c)

C ⊂ A

d)

A ⊂ B

51.

Which of the following sets has 4 elements?

a)

A = { x/x is an odd number }

b)

B = { x/x is a vowel }

c)

C = {x/x is an even number between 1 to 9}

d)

D = {x/x is an even number from 2 to 10}

52.

A well-defined set is a group, list, or collection of easily identified objects that shared a common characteristic. Which of the following is NOT a well-defined set?

a)

group of Grade 7 female students

b)

color in the Philippine flag

c)

distinct letter in the word Philippines

d)

good senators in the Philippines

53.

If set A and set B are disjoint, how they are represented ?

a)

By overlapping

b)

By two non-intersecting circle

c)

With set A is drawn inside the circle representing set B

d)

With set B is drawn inside the circle representing set A

54.

If set A and set B are disjoint, how they are represented ?

a)

By overlapping

b)

By two non-intersecting circle

c)

With set A is drawn inside the circle representing set B

d)

With set B is drawn inside the circle representing set A

55.
What is the definition of function?
a)
Has inputs and outputs
b)
Every input has only ONE output
c)
Inputs have different outputs every time
d)
x-values and y-values
56.
All of the y values or outputs are called what?
a)
Domain
b)
Range
c)
Relation
d)
Function
57.
All of the x values or inputs are called what?
a)
Domain
b)
Range
c)
Relation
d)
Function
58.
Is the relation a function? Why.
a)
Yes, because the x-value 11 has two y-values pair with it.
b)
Yes, because each x-value has only one y-value paired with it.
c)
No, because the x-value 11 has two y-values pair with it.
d)
No, because each x-value has only one y-value paired with it.
59.
Which set of values is a function?
a)
(9,5) (10,5) (9,-5) (10,-5)
b)
(3,4) (4,-3) (7,4) (3, 8)
c)
(6,-5) (7, -3) (8, -1) (9, 1)
d)
(2, -2) (5, 9) (5, -7) (1, 4)
60.
Does the table represent a function?
a)
Yes, there  is a repeated x-value. 
b)
No, there aren't any repeated y-values. 
c)
Yes, there are repeated y-values. 
d)
No, there is a repeated x-value. 
61.
Which graph does NOT pass the vertical line test?
a)
Graph 1
b)
Graph 2
c)
Graph 3
d)
Graph 4
62.
a)

Injective

b)

Bijective

c)

Surjective

63.
a)

Bijective

b)

Surjective

c)

Injective

64.

Which numbers belong to injective?

a)

(i) and (ii)

b)

(ii) and (iv)

c)

(i) and (iii)

d)

(ii) and (iii)

65.

What kind of function is it?

a)

Injective / One to One

b)

Surjective / Onto

c)

Bijective / One-to-one correspondence

66.

1.Let f be a function on set A = {1,2,3,4,5} such that f = {(1,2) (2,3),(3,4) (4,2) ,(5, 5) }

a)

f is one - one function

b)

f is onto function

c)

f is bijective function

d)

none of the above

67.

2.Let f be a function on set A = {1,2,3,4,5} such that f = {(1,2) (2,3),(3,4) (4,x) ,(5, 5) }. If f is bijective function then value of x =

a)

5

b)

3

c)

1

d)

none of these

68.

13. f: N→N given by f(x)=x^2 is

a)

one one

b)

not one one

c)

onto

d)

bijective

69.

14. f : Z → Z given by f (x) = x^2 is

a)

one one

b)

onto

c)

neither one one nor onto

d)

bijective

70.

1.Let f be a function on set A = {1,2,3,4,5} such that f = {(1,2) (2,3),(3,4) (4,2) ,(5, 5) }

a)

f is one - one function

b)

f is onto function

c)

f is bijective function

d)

none of the above

71.

2.Let f be a function on set A = {1,2,3,4,5} such that f = {(1,2) (2,3),(3,4) (4,x) ,(5, 5) }. If f is bijective function then value of x =

a)

5

b)

3

c)

1

d)

none of these

72.

3. Let f be a function on set A = {1,2,3,4,5} such that f = {(1,1) (2,2),(3,3) (4,4) ,(5, 5) }

a)

f is injective but not surjective

b)

f is surjective but not injective

c)

f is bijective

d)

none of the above

73.

4. Let A = {4,5,6,7 } , B = {4,5,6,7 } .f is a one - one function from A to B. Which of the following is correct

a)

f is into function

b)

f is bijective function

c)

f may or may not be bijective function

d)

question out of syllabus

74.

5. Let A = {7, 8 ,9 } , B = {7 , 8 , 9 } .f is onto function from A to B. Which of the following is correct

a)

f is not one - one function

b)

f may be one - one or many one

c)

f is injective function

d)

none of the above

75.

6. f: A →B. If f is onto function then

a)

A=B

b)

A is subset of B

c)

Range of f =A

d)

range of f = B

76.

7. f : A → B . If f is one-one function then

a)

Number of elements in range of f = n(B)

b)

n(A) = n(B)

c)

number of elements in range of f = n(A)

d)

n(A) > number of elements in range of f

77.

8. f : A → B . If f is bijective function then which of the following is true

a)

Number of elements in range of f = n(A)

b)

Number of elements in range of f = n(B)

c)

n(A) = n(B)

d)

All of the above

78.

9. f : A → B . If f is a bijective function and n(A) = 6 then which of following is not possible

a)

Number of elements in the range of f = 6

b)

n(B) = 6

c)

n(B) =8

d)

none of the above

79.

10. If f(a)=f(b) implies that a=b then f is

a)

not one one

b)

one one

c)

not onto

d)

onto

80.

f:[0,π]→R given by f(x)=sinx is

a)

one one

b)

onto

c)

not one one

d)

bijective

81.

12. f:R→R given by f(x)=2x is

a)

only one one

b)

only onto

c)

neither one one nor onto

d)

bijective

82.

13. f: N→N given by f(x)=x^2 is

a)

one one

b)

not one one

c)

onto

d)

bijective

83.

14. f : Z → Z given by f (x) = x^2 is

a)

one one

b)

onto

c)

neither one one nor onto

d)

bijective

84.

15. f : R → R given by f (x) = sin x is

a)

one one

b)

onto

c)

bijective

d)

neither one one nor onto

85.
Find the inverse of f(x) = -4x - 12
a)
f-1(x) = 4x - 3
b)
f-1(x) = -1/4x - 3
c)
f-1(x) = 1/4x + 3
d)
f-1(x) = -4x - 3
86.

Are the following inverses of each other? Use composition of functions. fog(x) and gof(x)

a)

True

b)

False

87.
Was the inverse function found correctly?
a)
no,
b)
yes
88.
Find the inverse of
f(x) = 1/4x - 7
a)
f-1(x) = 4x + 7
b)
f-1(x) = -4x + 28
c)
f-1(x) = -4x - 7
d)
f-1(x) = 4x + 28
89.
Find the inverse of the function
f(x) = 3x − 5
a)
f-1(x)=3x +5
b)
f-1(x)=(x+5)/3
c)
f-1(x)=3y-5
d)
f-1(x)=3y+5
90.
What does it mean to find the inverse of a function?
a)
the x's and y's are switched
b)
the x's and y's are divided by 2
c)
the x's and y's are made negative
d)
the x's and y's are the same
91.

If f(x)=x+5, what is f-1(x)?

a)

(x + 5)2

b)

x - 5

c)

(x + 5)-1

d)

undefined

92.

If f(x)=3x, what is f-1(x)?

a)

x/3

b)

3x2

c)

3x + 3x

d)

3x-1

93.

f(x) = 3x + 10

g(x) = ⅓x - 3

Find g(f(x))

a)

f(g(x)) = 1

b)

f(g(x)) = x

c)

f(g(x)) = 0

d)

None of these.

94.
a)

Inverse Functions

b)

Not Inverse Functions

95.
a)

Inverse Functions

b)

Not Inverse Functions

96.
a)

Inverse Functions

b)

Not Inverse Functions

97.
a)
Inverse Functions
b)
Not Inverse Functions
98.

What operation allows us to verify if functions are inverses?

a)

Multiplying

b)

Dividing

c)

Adding

d)

Composing

99.

What does an inverse function do?

a)

Nothing

b)

Makes it bigger

c)

Does the opposite of the original function

100.
What is the inverse of this function?
a)
A
b)
B
c)
C
d)
D
101.
What is the inverse of the points (1,3)(2,4)(6,2)
a)
(2,6)(3,1)(4,2)
b)
(-3,-1)(-4,-2)(-2,-6)
c)
(1,3)(2,4)(6,2)
d)
(-1,-3)(-2,-4)(-6,-2)
102.
Find the inverse 
f(x)=2x-2
     
a)
f-1(x)=1/2x+1
b)
f-1(x)=-2-1/2x
c)
f-1(x)=-7/3x-20/3
d)
2-2/5x
103.
Find the inverse 
f(x)=2x-2
     
a)
f-1(x)=1/2x+1
b)
f-1(x)=-2-1/2x
c)
f-1(x)=-7/3x-20/3
d)
2-2/5x
104.
Find the inverse 
f(x)= x- 2
a)
∜(x+2)
b)
(x+2)4
c)
-1+2x4
d)
∜2x
105.
What does it mean to find the inverse of a function?
a)
the x's and y's are switched
b)
the x's and y's are divided by 2
c)
the x's and y's are made negative
d)
the x's and y's are the same
106.
Find the inverse of f(x) = -4x - 12
a)
f-1(x) = 4x - 3
b)
f-1(x) = -1/4x - 3
c)
f-1(x) = 1/4x + 3
d)
f-1(x) = - 4x - 3
107.
If the equation of f(x) goes through (1, 4) and (4, 6), what points does f-1(x) go through?
a)
(1, 4) and (4, 6)
b)
(-4, -1) and (-6, -4)
c)
(-1, -4) and (-4, -6)
d)
(4, 1) and (6, 4)
108.
The inverse has been reflected over which line?
a)
y = x
b)
y =1
c)
y = 0
d)
y = x + 1
109.
When finding the inverse of a relation, 
1st you replace f(x) with y
2nd switch the x's and y's
What do you do next?
a)
solve for y
b)
replace y with f-1(x)
c)
solve for x
d)
find the greatest common factor
110.
Find the inverse of
f(x) = 1/4x - 7
a)
f-1(x) = 1/4x + 7/4
b)
f-1(x) = -4x + 28
c)
f-1(x) = -4x - 7
d)
f-1(x) = 4x + 28
111.
Find the inverse of f(x) = 5/11x +10 
a)
f-1(x) = 11/5(x - 10)
b)
f-1(x) = 5/11x - 22
c)
f-1(x) = 11/5x - 10
d)
None of the above
112.
Find the inverse of f(x) = -2/3x + 1/4
a)
f-1(x) = -3/2x + 3/8
b)
f-1(x) = 3/2x - 3/8
c)
f-1(x) = -3/2x + 8/3
d)
f-1(x) = 3/2x + 3/8
113.
Given that f(x) = 3x + 5 and g(x) = 1/3x + 5, find f(g(x)).  Are the two functions inverses of each other?
a)
x + 20 ; Yes they are inverses
b)
x + 20 ; No, they are not inverses
c)
x ; Yes they are inverses
d)
x ; No, they are not inverses
114.
What is the approximate solution to the equation 3x-1 = 42x + 5
a)
3.875
b)
1.262
c)
-2.354
d)
-4.797
115.
a)
A
b)
B
c)
C
d)
D
116.
a)
A
b)
B
c)
C
d)
D