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WorksheetsNotes on Sets
Total questions: 116
Worksheet time: 6hrs 22mins
List all the elements in A= {letters in the word "BOOK"}.
A= {B,O,K}
A= {B,O,O,K}
A= {B,K}
Which symbol completes the statement correctly? {6}____{1,3,6}
ϵ
⊂
=
⊂
Complete the statement correctly: Cow____ the set of all farm animals.
ϵ
⊂
⊆
⊂
Which of the following is a well-defined set?
{a happy child}
{a popular TV series}
{a favorite book by my classmates}
{a Mathematics book in the school library}
Which of these sets is equal to {L,O,V,E}?
{O,V,E}
{S,E,V,O,L}
{O,E,L,V}
{L,E,V}
Which of these sets is equivalent but not equal to {Ram, Jay, Mick}
{Mick, Jay, Olga}
{Jay, Mick, Ram}
{Mick, Jay, Ram}
{Andy, Ram, Ed, Jay}
Describe this set in words: {2,3,5,7,11,13,17,19}
Set of prime numbers from 2 to 19
Set of prime numbers less than 19
Set of odd numbers less than 20
Set of whole numbers less than 20
Which of the following statements is TRUE?
2 ϵ {1,3,5,7}
{5} ϵ {5,10,15,20,}
6 ϵ {x/x is an odd number}
3 ϵ {x/x is a prime number}
Consider M={vowels in the word "MATHEMATICS"}. Find n(M).
4
3
7
10
Write {even whole numbers between 3 to 15} using the roster method.
{3,5,7,9,11,13,15}
{5,7,9,11,13}
{4,6,8,10,12,14}
{2,4,6,8,10,12,14,16}
(a) is a collection of well-defined objects.
Another term for member of a set.
element
set
set notation
roster method
"The set of honest people" is a _____set.
well-defined
not well-defined
Which of the following is a well-defined set?
The set of beautiful flowers
The set of nice cars
The set of good students
The set of books in a shelf
Which of these is an empty set?
The set of green apples.
The set of two-legged elephants
The set of white shirts
The set of green bananas
What is the cardinality of set A is a counting number less than 10?
7
8
9
10
Which of the following sets is infinite?
Set W is a counting number less than 5.
Set A is a set of whole number between 10 and 15.
Set Y is a set of letters in the English alphabet after U.
Set S is a set or prime numbers.
Which of the following is true?
The cardinality of an empty set is 1.
If two sets have exactly the same elements, then they are equal.
If two sets are equal, then they are equivalent.
If two sets are equivalent, then they are equal.
If two sets have exactly the same elements, then they are (a) .
If A = {a, b, c, d}, how many subsets does A have?
(a)
Which is not an infinite set?
{x|x is a counting number greater than 15}
{2, 4, 6,..}
{x|x is a factor of 36}
{x|x is a multiple of 9}
Which set has denumerable elements?
Universal Set
Empty Set
Infinite Set
Finite Set
What way of expressing sets lists down all the elements contained in the set?
set-builder
roster
graphical
semantic
What operation on sets combine all the elements found in the sets selected?
Union
Intersection
Complement
Cardinality
An instructive way of describing the relationships between sets and elements and are made up of circles which represent the sets.
Venn Diaphragm
Venn Diagram
Venn Euler
Venn Operations
Which of the following is set Q ?
What type of set is denoted as either { } or ∅?
Superset
Disjointed Set
Empty (or Null) Set
Subset
If A= {10,20,30,40},B={20,40,60} and C = {10,20,40,60,80}, find A Ո B Ո C
{20,40}
{20,40,60}
{10,20,30,40,50,60,80}
{10,20,30,...}
For the given sets A and B, which statement is true?
A ⊂ B
B ⊂ A
A = B
A' = B
Use the Venn diagram to identify the statement that is true.
2 ∈ P ∩ Q
5 ∈ Q
{5,7} ⊆ P
P U Q = Q
List the elements of (A U B)'
{1,4}
{2,3,5,6,7,8,9}
{2,3,6,7,8}
{5,9}
{ x | x is a Marymount Student}
Roster Form
Universal Form
Set Builder Notation
Equivalent Inequality
Which of the following statements are true for the Venn diagram shown?
Overlapping sets
Subsets
Disjoint sets
Equal sets
Which of the following statements are true for the Venn diagram shown?
A is a subset of B
B is a subset of A
A = B
A and B are disjoint sets
B is a superset of A
Determine if the following sets are:
Subsets
Equal sets
Overlapping sets
Disjoint sets
How many subsets will this set have? A= {a, b, c} ?
8
6
3
0
Every set has _____ as one of its subsets (select all that apply.)
∅
0
itself
the real numbers
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.
Not equal because seat has 4 letters and taste has 5 letters.
Equivalent because they have the same letters
Equal because each set has the same cardinality and the same letters.
Consider M={vowels in the word "MATHEMATICS"}. Find n(M).
4
3
7
10
Set D is the set of the distinct letters in the word mathematics. Write the set using the Roster method.
D = {m, a, t, h, e, m, a, t, i, c, s}
D = {m, a, t, h}
D = {m, a, t, h, e, i, c, s}
D = {m, a, t, h, i, c, s}
What is the cardinality of the set A = {whole numbers less than or equal to 20}?
20
21
19
18
Which is a subset of X={1, 2}?
{ }
{1}
{1,2}
{2}
all of the above
R = { factors of 36 }.
n(R) =
set V = { m, n, o, p },
find the number of subsets V.
Which of the following is not a well-defined set?
The set of boys in your class
The set of even numbers
The set of students wearing red dress
The set of the colors of the rainbow
The Universal set U= {the days of the week}, subset A= {Monday, Friday} what is A'?
A' = {Monday, Friday}
A'= {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
A'={Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
The group of intelligent students in a class is
A finite set
A null set
A singleton set
Not a well defined collection
The group of intelligent students in a class is
A finite set
A null set
A singleton set
Not a well defined collection
Let A = {2, 3, 4, 5, 6, 7}
B = {2, 4, 7, 8)
C = {2, 4}.
Which of the following mathematical statements is true?
B ⊂ C
A ⊂ C
C ⊂ A
A ⊂ B
Which of the following sets has 4 elements?
A = { x/x is an odd number }
B = { x/x is a vowel }
C = {x/x is an even number between 1 to 9}
D = {x/x is an even number from 2 to 10}
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?
group of Grade 7 female students
color in the Philippine flag
distinct letter in the word Philippines
good senators in the Philippines
If set A and set B are disjoint, how they are represented ?
By overlapping
By two non-intersecting circle
With set A is drawn inside the circle representing set B
With set B is drawn inside the circle representing set A
If set A and set B are disjoint, how they are represented ?
By overlapping
By two non-intersecting circle
With set A is drawn inside the circle representing set B
With set B is drawn inside the circle representing set A
Injective
Bijective
Surjective
Bijective
Surjective
Injective
Which numbers belong to injective?
(i) and (ii)
(ii) and (iv)
(i) and (iii)
(ii) and (iii)
What kind of function is it?
Injective / One to One
Surjective / Onto
Bijective / One-to-one correspondence
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) }
f is one - one function
f is onto function
f is bijective function
none of the above
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 =
5
3
1
none of these
13. f: N→N given by f(x)=x^2 is
one one
not one one
onto
bijective
14. f : Z → Z given by f (x) = x^2 is
one one
onto
neither one one nor onto
bijective
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) }
f is one - one function
f is onto function
f is bijective function
none of the above
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 =
5
3
1
none of these
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) }
f is injective but not surjective
f is surjective but not injective
f is bijective
none of the above
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
f is into function
f is bijective function
f may or may not be bijective function
question out of syllabus
5. Let A = {7, 8 ,9 } , B = {7 , 8 , 9 } .f is onto function from A to B. Which of the following is correct
f is not one - one function
f may be one - one or many one
f is injective function
none of the above
6. f: A →B. If f is onto function then
A=B
A is subset of B
Range of f =A
range of f = B
7. f : A → B . If f is one-one function then
Number of elements in range of f = n(B)
n(A) = n(B)
number of elements in range of f = n(A)
n(A) > number of elements in range of f
8. f : A → B . If f is bijective function then which of the following is true
Number of elements in range of f = n(A)
Number of elements in range of f = n(B)
n(A) = n(B)
All of the above
9. f : A → B . If f is a bijective function and n(A) = 6 then which of following is not possible
Number of elements in the range of f = 6
n(B) = 6
n(B) =8
none of the above
10. If f(a)=f(b) implies that a=b then f is
not one one
one one
not onto
onto
f:[0,π]→R given by f(x)=sinx is
one one
onto
not one one
bijective
12. f:R→R given by f(x)=2x is
only one one
only onto
neither one one nor onto
bijective
13. f: N→N given by f(x)=x^2 is
one one
not one one
onto
bijective
14. f : Z → Z given by f (x) = x^2 is
one one
onto
neither one one nor onto
bijective
15. f : R → R given by f (x) = sin x is
one one
onto
bijective
neither one one nor onto
Are the following inverses of each other? Use composition of functions. fog(x) and gof(x)
True
False
f(x) = 1/4x - 7
f(x) = 3x − 5
If f(x)=x+5, what is f-1(x)?
(x + 5)2
x - 5
(x + 5)-1
undefined
If f(x)=3x, what is f-1(x)?
x/3
3x2
3x + 3x
3x-1
f(x) = 3x + 10
g(x) = ⅓x - 3
Find g(f(x))
f(g(x)) = 1
f(g(x)) = x
f(g(x)) = 0
None of these.
Inverse Functions
Not Inverse Functions
Inverse Functions
Not Inverse Functions
Inverse Functions
Not Inverse Functions
What operation allows us to verify if functions are inverses?
Multiplying
Dividing
Adding
Composing
What does an inverse function do?
Nothing
Makes it bigger
Does the opposite of the original function
f(x)=2x-2
f(x)=2x-2
f(x)= x4 - 2
1st you replace f(x) with y
2nd switch the x's and y's
What do you do next?
f(x) = 1/4x - 7
