Quiz about SETS R.S AGRAWAL

Question 1

A well-defined collection of objects is called a ____.

Accepted Answer

set

Answer

group

Answer

array

Answer

list

Question 2

In the roster form, the order in which elements are listed is ____.

Accepted Answer

immaterial

Answer

important

Answer

fixed

Answer

alphabetical

Question 3

The set of all natural numbers is denoted by ____.

Accepted Answer

N

Answer

Z

Answer

Q

Answer

R

Question 4

The set of all integers is denoted by ____.

Accepted Answer

Z

Answer

I

Answer

N

Answer

Q

Question 5

The set of all rational numbers is denoted by ____.

Accepted Answer

Q

Answer

R

Answer

Z

Answer

N

Question 6

The set of all real numbers is denoted by ____.

Accepted Answer

R

Answer

Q

Answer

Z

Answer

N

Question 7

A set is said to be ____ if it contains no element.

Accepted Answer

empty/null/void

Answer

full

Answer

partial

Answer

infinite

Question 8

A set containing exactly one element is called a ____ set.

Accepted Answer

singleton

Answer

empty

Answer

finite

Answer

infinite

Question 9

An empty set or a set in which the process of counting elements comes to an end is called a ____ set.

Accepted Answer

finite

Answer

infinite

Answer

countable

Answer

uncountable

Question 10

Two sets A and B are said to be ____ if they have exactly the same elements.

Accepted Answer

equal

Answer

disjoint

Answer

complementary

Answer

overlapping

Question 11

Two finite sets A and B are said to be ____ if n(A) = n(B).

Accepted Answer

equivalent

Answer

disjoint

Answer

equal

Answer

subset

Question 12

A set A is a ____ of set B if every element of A is also an element of B.

Accepted Answer

subset

Answer

superset

Answer

intersection

Answer

union

Question 13

The set of all subsets of a given set A is called the ____ of A.

Accepted Answer

power set

Answer

subset

Answer

union

Answer

intersection

Question 14

The collection of all tall students in a class is a set.

Accepted Answer

False

Answer

True

Question 15

The collection of all vowels in the English alphabet is a set.

Accepted Answer

True

Answer

False

Question 16

In roster form, the order of elements matters.

Accepted Answer

False

Answer

True

Question 17

{1, 2, 3} and {3, 1, 2} represent the same set.

Accepted Answer

True

Answer

False

Question 18

The set-builder form lists all elements of the set.

Accepted Answer

False

Answer

True

Question 19

The empty set is denoted by {0}.

Accepted Answer

False

Answer

True

Question 20

{0} is an empty set.

Accepted Answer

False

Answer

True

Question 21

A singleton set has only one element.

Accepted Answer

True

Answer

False

Question 22

All sets are either finite or infinite.

Accepted Answer

True

Answer

False

Question 23

Equal sets are always equivalent.

Accepted Answer

True

Answer

False

Question 24

Equivalent sets are always equal.

Accepted Answer

False

Answer

True

Question 25

Every set is a subset of itself.

Accepted Answer

True

Answer

False

Question 26

The power set of a set with n elements has $$2^n$$ elements.

Accepted Answer

True

Answer

False

Question 27

The intersection of two sets is always a subset of their union.

Accepted Answer

True

Answer

False

Question 28

The complement of a set is always unique.

Accepted Answer

True

Answer

False

Question 29

Which of the following represents the set of all vowels in the English alphabet?

Accepted Answer

{a, e, i, o, u}

Answer

{a, b, c, d, e}

Answer

{a, b, i, o, u}

Answer

{a, e, i, y, u}

Question 30

What is the roster form of the set of all factors of 12?

Accepted Answer

{1, 2, 3, 4, 6, 12}

Answer

{1, 2, 3, 4, 6}

Answer

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

Answer

{3, 6, 9, 12}

Question 31

Which of the following is a singleton set?

Accepted Answer

{0}

Answer

{1, 2}

Answer

$${x : x \in R, x^2 = 4}$$

Answer

{}

Question 32

Which of the following is a finite set?

Accepted Answer

Set of all integers less than 100

Answer

Set of all points on a line

Answer

Set of all natural numbers

Answer

Set of all stars in the sky

Question 33

Which of the following is an infinite set?

Accepted Answer

Set of all letters in the English alphabet

Answer

Set of all days in a week

Question 34

Which of the following is a proper subset of {1, 2, 3}?

Accepted Answer

{ }

Answer

{1, 2, 3}

Answer

{1, 2, 4}

Answer

All of the above

Question 35

The power set of {1, 2} is:

Accepted Answer

{{1}, {2}, {1, 2}}

Answer

{{1, 2}}

Answer

{{1}, {2}}

Answer

{{ }, {1}, {2}, {1, 2}}

Question 36

If A = {1, 2, 3}, how many subsets does A have?

Accepted Answer

8

Answer

3

Answer

6

Answer

9

Question 37

Instructions: In the following questions, Assertion (A) and Reason (R) are given. Choose the correct option: (a) Both A and R are true and R is the correct explanation of A (b) Both A and R are true but R is not the correct explanation of A (c) A is true but R is false (d) A is false but R is true. Assertion (A): {1, 2, 3} = {3, 2, 1} Reason (R): The order of elements in a set does not matter.

Accepted Answer

Both A and R are true and R is the correct explanation of A

Answer

Both A and R are true but R is not the correct explanation of A

Answer

A is true but R is false

Answer

A is false but R is true

Question 38

Instructions: In the following questions, Assertion (A) and Reason (R) are given. Choose the correct option: (a) Both A and R are true and R is the correct explanation of A (b) Both A and R are true but R is not the correct explanation of A (c) A is true but R is false (d) A is false but R is true. Assertion (A): {1, 1, 2, 2} = {1, 2} Reason (R): Repetition of elements in a set has no meaning.

Accepted Answer

Both A and R are true and R is the correct explanation of A

Answer

Both A and R are true but R is not the correct explanation of A

Answer

A is true but R is false

Answer

A is false but R is true

Question 39

Assertion (A): Empty set is a singleton set. Reason (R): A set containing only one element is called a singleton set.

Accepted Answer

A is false but R is true

Answer

Both A and R are true and R is the correct explanation of A

Answer

Both A and R are true but R is not the correct explanation of A

Answer

A is true but R is false

Question 40

Assertion (A): The set of all natural numbers is a finite set. Reason (R): A set which is not finite is called an infinite set.

Accepted Answer

A is false but R is true

Answer

Both A and R are true and R is the correct explanation of A

Answer

Both A and R are true but R is not the correct explanation of A

Answer

A is true but R is false

Question 41

Explain the difference between a set and a collection.

Accepted Answer

A set is a type of collection that does not allow duplicate elements, while a collection can have duplicates.

Answer

A collection is a type of set that does not allow duplicate elements, while a set can have duplicates.

Answer

A set and a collection are the same, with no differences.

Answer

A set allows duplicate elements, while a collection does not.

Question 42

Which of the following is an example of a well-defined set?

Accepted Answer

The set of all prime numbers

Answer

The set of all tall people

Answer

The set of all beautiful paintings

Answer

The set of all interesting books

Question 43

Which of the following is an example of a collection that is not a set and why?

Accepted Answer

A list because it can contain duplicate elements.

Answer

A set because it contains unique elements.

Answer

A dictionary because it has key-value pairs.

Answer

A tuple because it is immutable.

Question 44

The importance of the "well-defined" criterion for a set is:

Accepted Answer

It ensures that the set is clearly defined and unambiguous.

Answer

It allows for the set to have multiple interpretations.

Answer

It makes the set more complex and difficult to understand.

Answer

It is not necessary for the definition of a set.

Question 45

The two methods of representing a set are:

Accepted Answer

Roster method and Set-builder method

Answer

Venn diagram and Tree diagram

Answer

Graphical method and Tabular method

Answer

Algebraic method and Numerical method

Question 46

The difference between roster form and set-builder form is:

Accepted Answer

Roster form lists all the elements of a set, whereas set-builder form describes the properties of the elements of the set.

Answer

Roster form describes the properties of the elements of the set, whereas set-builder form lists all the elements of a set.

Answer

Both forms list all the elements of a set.

Answer

Both forms describe the properties of the elements of the set.

Question 47

A set can have another set as its element. Can you identify an example of this?

Accepted Answer

{1, 2, {3, 4}}

Answer

{1, 2, 3, 4}

Answer

{1, {2, 3}, 4}

Answer

{1, 2, 3, {4}}

Question 48

The concept of an empty set is:

Accepted Answer

A set with no elements

Answer

A set with one element

Answer

A set with infinite elements

Answer

A set with two elements

Question 49

Is { } the same as {0}?

Accepted Answer

No, { } is not the same as {0}.

Answer

Yes, { } is the same as {0}.

Answer

It depends on the context.

Answer

Cannot be determined.

Question 50

A singleton set is a set containing exactly one element. Which of the following is an example of a singleton set?

Accepted Answer

{a}

Answer

{1, 2}

Answer

{}

Answer

{1, 2, 3}

Question 51

Differentiate between a finite and an infinite set.

Accepted Answer

A finite set has a limited number of elements, while an infinite set has unlimited elements.

Answer

A finite set has unlimited elements, while an infinite set has a limited number of elements.

Answer

Both finite and infinite sets have unlimited elements.

Answer

Both finite and infinite sets have a limited number of elements.

Question 52

Which of the following are examples of finite and infinite sets?

Accepted Answer

A set of all vowels in the English alphabet and a set of all real numbers

Answer

A set of all natural numbers and a set of all even numbers

Answer

A set of all prime numbers and a set of all odd numbers

Answer

A set of all whole numbers and a set of all integers

Question 53

What are equal sets? Give examples.

Accepted Answer

Sets that have exactly the same elements

Answer

Sets that have the same number of elements

Answer

Sets that have different elements

Answer

Sets that are subsets of each other

Question 54

If A = {1, 2, 3, 4} and B = {2, 4, 6, 8}, which elements are common to both A and B?

Accepted Answer

{2, 4}

Answer

{1, 3}

Answer

{6, 8}

Answer

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

Question 55

The union of A = {1, 2} and B = {2, 3} is:

Accepted Answer

{1, 2, 3}

Answer

{2}

Answer

{1, 3}

Answer

{}

Question 56

What is the complement of the universal set U?

Accepted Answer

{}

Answer

U

Answer

U

Answer

1

Question 57

If U = {1, 2, 3, 4, 5} and A = {1, 3}, then A' (complement of A) is:

Accepted Answer

{2, 4, 5}

Answer

{1, 3}

Answer

{1, 2, 3, 4, 5}

Answer

{}

Question 58

A - B is the set of elements which belong to:

Accepted Answer

A only

Answer

B only

Answer

Both A and B

Answer

None of A or B

Question 59

If A = {1, 2, 3} and B = {2, 3, 4}, then A - B is:

Accepted Answer

{1}

Answer

{1, 2, 3, 4}

Answer

{2, 3}

Answer

{4}

Question 60

The number of elements in the power set of the empty set is:

Accepted Answer

1

Answer

0

Answer

2

Answer

Infinite

Question 61

Assertion (A): The power set of $${1, 2, 3}$$ has 6 elements. Reason (R): The power set of a set with $$n$$ elements has $$2^n$$ elements.

Accepted Answer

d

Answer

a

Answer

b

Answer

c

Question 62

In a class of 30 students, 20 like cricket and 15 like football. How many like both cricket and football?

Accepted Answer

5

Answer

0

Answer

10

Answer

15

Question 63

In a survey of 100 people, 50 like coffee and 40 like tea, and 20 like both. How many like neither?

Accepted Answer

30

Answer

10

Answer

20

Answer

40

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