If $A = \{x : x \text{ is a letter in the word 'EQUATION'}\}$, what is the set $A$?

Correct Option: A. Solution: The set of letters in the word 'EQUATION' is $\{E, Q, U, A, T, I, O, N\}$.

Sets

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Summary

Chapter Summary: Sets

Introduction

Sets are fundamental in modern mathematics, used in various branches including geometry, probability, and functions.
Developed by Georg Cantor (1845-1918).

Basic Definitions

Set: A well-defined collection of objects.
Empty Set: A set with no elements, denoted as Φ.
Finite Set: A set with a definite number of elements.
Infinite Set: A set that is not finite.
Equal Sets: Two sets A and B are equal if they contain the same elements.
Subset: A set A is a subset of B if every element of A is also in B.

Set Operations

Union (A ∪ B): The set of elements in A or B.
Intersection (A ∩ B): The set of elements common to both A and B.
Difference (A - B): The set of elements in A but not in B.
Complement (A'): The set of elements not in A, relative to a universal set U.

Important Laws

De Morgan's Laws:
- (A ∪ B)' = A' ∩ B'
- (A ∩ B)' = A' ∪ B'

Venn Diagrams

Used to represent relationships between sets visually.

Examples of Sets

Odd natural numbers less than 10: {1, 3, 5, 7, 9}
Rivers of India
Vowels in the English alphabet: {a, e, i, o, u}
Prime factors of 210: {2, 3, 5, 7}
Solutions of x² - 5x + 6 = 0: {2, 3}

Historical Note

Georg Cantor's work on set theory began in the 1870s, focusing on properties of sets and their cardinalities.

Learning Objectives

Understand the concept of sets as a fundamental part of mathematics.
Identify and represent different types of sets, including finite and infinite sets.
Distinguish between roster form and set-builder form for representing sets.
Define and identify subsets and proper subsets.
Recognize the concept of the empty set and its properties.
Perform operations on sets, including union, intersection, and difference.
Utilize Venn diagrams to represent relationships between sets.
Apply the definitions and properties of sets to solve mathematical problems.

Detailed Notes

Chapter 1: Sets

1.1 Introduction

The concept of set is fundamental in mathematics, used in various branches like geometry, sequences, and probability.
Developed by Georg Cantor (1845-1918) while working on trigonometric series.

1.2 Sets and their Representations

Collections of objects in mathematics are called sets.
Examples of sets:
- Odd natural numbers less than 10: {1, 3, 5, 7, 9}
- Rivers of India
- Vowels in the English alphabet: {a, e, i, o, u}
- Prime factors of 210: {2, 3, 5, 7}
- Solutions of the equation x² - 5x + 6 = 0: {2, 3}

1.3 The Empty Set

A set with no elements is called the empty set (Φ).

1.6 Subsets

A set A is a subset of set B (A ⊆ B) if every element of A is also in B.
Example: If X = set of all students in a school, and Y = set of all students in a class, then Y ⊆ X.

1.7 Universal Set

The universal set (U) contains all elements relevant to a particular context.
Example: For integers, U can be the set of rational numbers.

1.8 Venn Diagrams

Venn diagrams visually represent relationships between sets using circles and rectangles.
The universal set is represented by a rectangle, and subsets by circles.

1.9 Operations on Sets

Basic operations include:
- Union (A ∪ B): Elements in A or B.
- Intersection (A ∩ B): Elements common to both A and B.
- Difference (A - B): Elements in A but not in B.
- Complement (A'): Elements not in A but in the universal set U.

Summary

A set is a well-defined collection of objects.
An empty set contains no elements.
A finite set has a definite number of elements; otherwise, it is infinite.
Two sets are equal if they have the same elements.
Subset definition: A is a subset of B if every element of A is in B.
Union, intersection, and difference operations are fundamental in set theory.

Exam Tips & Common Mistakes

Common Mistakes and Exam Tips

Common Pitfalls

Misunderstanding Set Notation: Students often confuse the symbols for subset (⊆) and element of (∈). Ensure clarity on these symbols.
Empty Set Confusion: The empty set (∅) is a valid set but contains no elements. Misidentifying it can lead to incorrect conclusions about set membership.
Incorrect Set Equality: Remember that two sets are equal only if they contain exactly the same elements, regardless of order or repetition.
Venn Diagram Misinterpretation: Students may misinterpret Venn diagrams, especially in identifying intersections and unions. Pay close attention to the shaded areas representing these operations.

Tips for Success

Practice Set Operations: Regularly practice problems involving union, intersection, and difference of sets to build familiarity.
Use Clear Examples: When defining sets, use clear and specific examples to avoid ambiguity.
Double-Check Complements: When finding complements, ensure you are referencing the correct universal set to avoid errors.
Review Definitions: Regularly review definitions of key terms such as subset, universal set, and empty set to reinforce understanding.

Practice & Assessment

Multiple Choice Questions

\{1, 3, 5\}

\{3, 5\}

\{1, 4\}

\{2, 4\}

Correct Answer: B

Solution:

The intersection of two sets is the set of elements that are common to both sets. Here,

\{3, 5\}

are common to both

A

and

B

{1, 2, 3, 4, 5}

{3}

{1, 2}

{4, 5}

Correct Answer: A

Solution:

The union of two sets

A

and

B

, denoted

A \cup B

, is the set of elements that are in

A

, in

B

, or in both. Here,

A \cup B = \{1, 2, 3, 4, 5\}

{-2, -1, 0, 1, 2}

{-2, 0, 2}

{-1, 0, 1}

{0, 1, 2}

Correct Answer: A

Solution:

The inequality

x^2 \leq 4

means

x

can be any number between -2 and 2 inclusive, hence the solution set is {-2, -1, 0, 1, 2}.

\{1, 2\}

\{3, 4\}

\{5, 6\}

\{1, 2, 5, 6\}

Correct Answer: A

Solution:

The set

A - B

consists of elements that are in

A

but not in

B

, which are

1

and

2

\{E, U, A, I, O\}

\{E, D, U, C, A, T, I, O, N\}

\{E, A, I\}

\{E, U, A\}

Correct Answer: A

Solution:

The vowels in the word 'EDUCATION' are E, U, A, I, and O. Therefore, the set

A

\{E, U, A, I, O\}

{6}

{2, 4, 6, 8, 10, 3, 9, 12}

{6, 12}

{2, 3, 4, 6, 8, 9, 10, 12}

Correct Answer: D

Solution:

The union of sets

A

and

B

includes all elements from both sets without repetition. Thus,

A \cup B = \{2, 3, 4, 6, 8, 9, 10, 12\}

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

{1, 3, 5, 7, 9}

{2, 4, 6, 8, 10}

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

Correct Answer: A

Solution:

The union of sets

A

and

B

includes all elements from both sets, hence

A \cup B = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}

{T, R, I, G, O, N, M, E, Y}

{T, R, I, G, O, N, E, M, Y, T}

{T, R, I, G, O, N, M, E}

{T, R, I, G, O, N, M, E, Y, R}

Correct Answer: A

Solution:

The set

A

contains the distinct letters in the word 'TRIGONOMETRY', which are {T, R, I, G, O, N, M, E, Y}.

{2, 4}

{4, 8}

{6, 8}

{2, 6}

Correct Answer: B

Solution:

The intersection of two sets

A

and

B

, denoted

A \cap B

, is the set of elements that are common to both

A

and

B

. Here,

A \cap B = \{4, 8\}

{2, 3}

{1, 6}

{2, 5}

{3, 4}

Correct Answer: A

Solution:

The equation

x^2 - 5x + 6 = 0

factors to

(x-2)(x-3) = 0

, so the solutions are

x = 2

and

x = 3

. Thus, the set is {2, 3}.

\{2, 4\}

\{1, 3\}

\{8, 10\}

\{5, 7\}

Correct Answer: A

Solution:

A subset is a set where all elements are contained within another set. Here,

\{2, 4\}

is a subset of

B

because both 2 and 4 are elements of

B

{A, E, I}

{A, E, I, O, U}

{M, T, H, C, S}

{A, I}

Correct Answer: A

Solution:

The set

A

consists of the letters in 'MATHEMATICS', which are {M, A, T, H, E, M, A, T, I, C, S}. The set

B

consists of vowels {A, E, I, O, U}. The intersection

A \cap B

includes vowels present in 'MATHEMATICS', i.e., {A, E, I}.

{2, 4, 6, 8, 10}

{1, 3, 5, 7, 9}

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

{6, 8, 10}

Correct Answer: A

Solution:

The complement of set

A

with respect to

U

is the set of elements in

U

that are not in

A

. Thus,

A' = \{2, 4, 6, 8, 10\}

Set

A

is finite.

Set

A

is infinite.

Set

A

is empty.

Set

A

is not well-defined.

Correct Answer: A

Solution:

The set

A

contains a finite number of students currently studying in Class XI, thus it is finite.

{1, 3, 5}

{2, 4, 6}

{7, 9, 11}

{12, 14, 16}

Correct Answer: B

Solution:

A set

A

is a subset of

B

if every element of

A

is also an element of

B

. Here,

\{2, 4, 6\}

is a subset of

B

because all its elements are in

B

\{1, 2, 3\}

and

\{4, 5, 6\}

\{2, 4, 6\}

and

\{1, 2, 3\}

\{3, 5, 7\}

and

\{5, 7, 9\}

\{0, 2, 4\}

and

\{1, 3, 5\}

Correct Answer: A

Solution:

Two sets are disjoint if they have no elements in common. The sets

\{1, 2, 3\}

and

\{4, 5, 6\}

have no common elements.

\{2, 4, 6, 8\}

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

\{2, 3, 5, 7\}

\{0, 2, 4, 6, 8, 10\}

Correct Answer: A

Solution:

The even natural numbers less than 10 are 2, 4, 6, and 8. Therefore, the set

B

\{2, 4, 6, 8\}

\{M, A, T, H, E, I, C, S\}

\{M, A, T, H, E, I, C\}

\{M, A, T, H, E, I, C, S, T\}

\{M, A, T, H, E, I\}

Correct Answer: A

Solution:

The set

A

consists of all unique letters in the word 'MATHEMATICS'. Thus,

A = \{M, A, T, H, E, I, C, S\}

{1, 2, 3} \text{ and } {4, 5, 6}

{2, 4, 6} \text{ and } {1, 2, 3}

{a, e, i} \text{ and } {o, u}

{x : x \text{ is an even number}} \text{ and } {x : x \text{ is an odd number}}

Correct Answer: D

Solution:

Two sets are disjoint if they have no elements in common. The set of even numbers and the set of odd numbers have no common elements, making them disjoint.

A = \{M, A, T, H, E, I, C, S\}

A = \{M, A, T, H, E, I, C\}

A = \{M, A, T, H, E, I\}

A = \{M, A, T, H, E, I, C, S, T\}

Correct Answer: A

Solution:

The set

A

includes all distinct letters in the word 'MATHEMATICS'. Repeated letters are not listed more than once.

{1, 4, 6}

{2, 3, 5}

{1, 2, 3}

{4, 5, 6}

Correct Answer: A

Solution:

The complement of a set

A

with respect to a universal set

U

is the set of elements in

U

that are not in

A

. Thus,

A' = \{1, 4, 6\}

\{3, 5, 6, 9, 10, 12, 15\}

\{3, 6, 9, 12, 15\}

\{5, 10, 15\}

\{3, 5, 6, 9, 10, 12\}

Correct Answer: A

Solution:

Set

A = \{3, 6, 9, 12, 15\}

and set

B = \{5, 10, 15\}

. The union

A \cup B = \{3, 5, 6, 9, 10, 12, 15\}

\{1, 2, 3, 4, 5\}

\{0, 1, 2, 3, 4, 5\}

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

\{2, 3, 4, 5\}

Correct Answer: A

Solution:

The set

C

includes all natural numbers less than 6, which are

\{1, 2, 3, 4, 5\}

{4, 5, 8, 10, 12, 15, 16, 20}

{4, 8, 12, 16, 20}

{5, 10, 15, 20}

{4, 5, 8, 10, 12, 16, 20}

Correct Answer: A

Solution:

Set

A = \{4, 8, 12, 16, 20\}

and set

B = \{5, 10, 15, 20\}

. The union

A \cup B

is the set of all elements that are in either

A

B

, which are

\{4, 5, 8, 10, 12, 15, 16, 20\}

The set of all natural numbers.

The set of all even numbers.

The set of all prime numbers less than 20.

The set of all integers.

Correct Answer: C

Solution:

A finite set has a definite number of elements. The set of all prime numbers less than 20 is finite because it includes exactly the numbers 2, 3, 5, 7, 11, 13, 17, and 19.

The collection of all intelligent students in a class

The collection of all vowels in the English alphabet

The collection of all beautiful paintings

The collection of all tall buildings

Correct Answer: B

Solution:

A well-defined set is one where it is clear whether an object belongs to the set or not. The collection of all vowels in the English alphabet is a well-defined set.

\{2\}

\{2, 4, 6, 8\}

\{2, 3, 5\}

\{\}

Correct Answer: A

Solution:

The intersection of sets

A

and

B

is the set of elements that are common to both. The only even prime number is 2, so

A \cap B = \{2\}

{L, O, Y, A}

{L, O, Y, A, L}

{L, O, Y}

{L, O, Y, A, L, Y}

Correct Answer: A

Solution:

The set

A

includes each letter in the word 'LOYAL' without repetition, so

A = \{L, O, Y, A\}

\in

\notin

\subseteq

\supseteq

Correct Answer: B

Solution:

The number 8 is not an element of set

A

. Therefore, the correct symbol is

\notin

{1, 3}

{2, 4}

{1, 2, 3, 4}

{3, 4}

Correct Answer: A

Solution:

The set

A

consists of natural numbers less than 5, which are {1, 2, 3, 4}. The set

B

consists of even natural numbers less than 5, which are {2, 4}. The difference

A - B

includes elements in

A

that are not in

B

, i.e., {1, 3}.

{M, A, T, H, E, I, C, S}

{M, A, T, H, E, I, C}

{M, A, T, H, E, I, C, S, M}

{M, A, T, H, E, I, C, S, T}

Correct Answer: A

Solution:

The set

A

includes all unique letters in the word 'MATHEMATICS'. Therefore,

A = \{M, A, T, H, E, I, C, S\}

{2}

{2, 4, 6, 8, 10, 12, 14, 16, 18}

{2, 3, 5, 7, 11, 13, 17, 19}

{}

Correct Answer: A

Solution:

The set

A

contains prime numbers less than 20: {2, 3, 5, 7, 11, 13, 17, 19}. The set

B

contains even numbers less than 20: {2, 4, 6, 8, 10, 12, 14, 16, 18}. The intersection

A \cap B

is {2}, as 2 is the only number that is both prime and even.

{2, 4, 6, 8, ...}

{1, 3, 5, 7, ...}

{0, 2, 4, 6, ...}

{1, 2, 3, 4, ...}

Correct Answer: A

Solution:

The set of all even natural numbers is represented by {2, 4, 6, 8, ...}.

\{a, e, i, o, u\}

\{b, c, d, f\}

\{a, e, i, o\}

\{a, e, i, o, u, y\}

Correct Answer: A

Solution:

The vowels in the English alphabet are

a, e, i, o, u

. Thus, the set

C

\{a, e, i, o, u\}

{2, 3, 5, 7}

{1, 3, 5, 7, 9}

{3, 5, 7}

{}

Correct Answer: C

Solution:

The intersection of sets

A

and

B

A \cap B

, is the set of elements that are common to both

A

and

B

. Here,

A \cap B = \{3, 5, 7\}

, as these are the numbers that are both prime and odd.

\{-3, 3\}

\{3\}

\{-3\}

\{0, 3\}

Correct Answer: A

Solution:

The set

A = \{x : x^2 = 9\}

includes all

x

such that when squared, the result is 9. Both

-3

and

3

satisfy this condition.

The empty set is a subset of every set.

The empty set is not a subset of any set.

The empty set contains one element.

The empty set is equal to every set.

Correct Answer: A

Solution:

The empty set, denoted by

\emptyset

, is a subset of every set because there are no elements in the empty set that are not in any other set.

{0, 1, 2}

{1, 2}

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

{}

Correct Answer: A

Solution:

Set

A

includes integers from -3 to 2: {-3, -2, -1, 0, 1, 2}. Set

B

includes natural numbers less than 5: {1, 2, 3, 4}. The intersection

A \cap B

is {0, 1, 2}, as these are the common elements.

{1, 2, 3, 4, 5}

{0, 1, 2, 3, 4, 5}

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

{2, 3, 4, 5, 6}

Correct Answer: A

Solution:

The natural numbers less than 6 are 1, 2, 3, 4, and 5. Therefore,

A = \{1, 2, 3, 4, 5\}

\{2, 4\}

\{6, 7\}

\{0, 1\}

\{3, 6\}

Correct Answer: A

Solution:

A subset of

A

is a set where all its elements are also in

A

. The set

\{2, 4\}

is a subset of

A

\{E, Q, U, A, T, I, O, N\}

\{E, Q, U, A, T, I, O\}

\{E, Q, U, A, T, I, O, N, S\}

\{E, Q, U, A, T, I\}

Correct Answer: A

Solution:

The set of letters in the word 'EQUATION' is

\{E, Q, U, A, T, I, O, N\}

{1, 2, 3}

{4, 5, 6}

{7, 8, 9}

{}

Correct Answer: B

Solution:

The intersection of two sets

A

and

B

is the set of all elements which are common to both sets. Here,

A \cap B = \{4, 5, 6\}

A \cup B = \{1, 2, 3, 4, 5\}

A \cup B = \{1, 2, 3\}

A \cup B = \{3, 4, 5\}

A \cup B = \{1, 5\}

Correct Answer: A

Solution:

The union of two sets

A

and

B

, denoted

A \cup B

, is the set of all elements that are in

A

, or

B

, or in both. Thus,

A \cup B = \{1, 2, 3, 4, 5\}

{1, 2}

{3, 4, 5}

{6, 7}

{1, 2, 6, 7}

Correct Answer: A

Solution:

The set

A = \{1, 2, 3, 4, 5\}

and set

B = \{3, 4, 5, 6, 7\}

. The difference

A - B

is the set of elements in

A

that are not in

B

, which is

\{1, 2\}

{a, e, i}

{a, b, c}

{x, y, z}

{a, e, i, o, u, y}

Correct Answer: A

Solution:

The set of vowels in the English alphabet is

\{a, e, i, o, u\}

. The set

\{a, e, i\}

is a subset of this set.

{1, 4, 6, 8, 9, 10}

{2, 3, 5, 7}

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

{}

Correct Answer: A

Solution:

The complement of a set

A

with respect to a universal set

U

is the set of elements in

U

that are not in

A

. Thus,

A' = \{1, 4, 6, 8, 9, 10\}

\{1, 2\}

\{3, 4\}

\{5, 6\}

\{1, 6\}

Correct Answer: B

Solution:

The intersection of two sets

A

and

B

, denoted

A \cap B

, is the set of elements that are common to both

A

and

B

. Here,

\{3, 4\}

are common to both sets.

The set of all natural numbers

The set of all prime numbers less than 99

The set of all integers

The set of all real numbers

Correct Answer: B

Solution:

The set of all prime numbers less than 99 is finite because it contains a limited number of elements.

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

{2, 4, 6, 8}

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

{}

Correct Answer: C

Solution:

The union of sets

A

and

B

A \cup B

, is the set of all elements that are in either

A

B

or in both. Here,

A \cup B = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}

{A, E}

{A, E, I, O, U}

{A, E, B, R}

{L, G, B, R}

Correct Answer: A

Solution:

The set

A = \{A, L, G, E, B, R\}

and the set

B = \{A, E, I, O, U\}

. The intersection

A \cap B

consists of elements common to both sets, which are

\{A, E\}

True or False

Correct Answer: False

Solution:

The set of all prime numbers is infinite because there is no largest prime number; primes continue indefinitely.

Correct Answer: True

Solution:

The difference

A - B

is defined as the set of elements that are in

A

Solution:

A set

A

being a subset of a set

B

means every element of

A

is in

B

, but not necessarily every element of

B

is in

Solution:

If every element of

A

is in

B

and every element of

B

is in

A

, then the sets have exactly the same elements, so

A = B

Correct Answer: True

Solution:

The excerpt mentions that the theory of sets was developed by German mathematician Georg Cantor.

Correct Answer: True

Solution:

The complement of a set

A

is defined as the set of all elements in the universal set

U

that are not in

A

B

are equal if they contain exactly the same elements, which implies that

A \subseteq B

and

B \subseteq A

Solution:

The excerpt defines the union of two sets

A

and

B

as the set of all those elements which are either in

A

Solution:

A finite set is one that contains a definite number of elements. The set of natural numbers less than 10 is {1, 2, 3, 4, 5, 6, 7, 8, 9}, which is finite.

Correct Answer: False

Solution:

The union of two sets

A

and

B

is the set of all elements which are either in

A

or in

B

, not just the common elements.

Correct Answer: True

Solution:

A null set is a set with no elements. Since no odd natural number can be divisible by 2, the set is empty.

Correct Answer: True

Solution:

The excerpt states that the concept of set serves as a fundamental part of present-day mathematics and is used in almost every branch.

Correct Answer: True

Solution:

By the transitive property of subsets, if every element of set

A

is in set

B

and every element of set

B

is in set

C

, then every element of set

A

must also be in set

C

. Thus,

A \subseteq C

Correct Answer: True

Solution:

Two sets are considered equal if they contain exactly the same elements, regardless of the order of the elements.

Correct Answer: True

Solution:

A

is a subset of

B

, then every element of

A

is also in

B

. Therefore, the union of

A

and

B

is just

B

A \cup B = B

Correct Answer: True

Solution:

Sets are fundamental in mathematics and are used to define relations and functions, as stated in the provided excerpt.

Correct Answer: False

Solution:

A set with no elements is called an empty set, not a finite set.

Correct Answer: True

Solution:

A set is defined as a well-defined collection of objects, meaning that it is clear whether an object belongs to the set or not.

Correct Answer: True

Solution:

This is known as De Morgan's law:

(A \cup B)' = A' \cap B'

Correct Answer: True

Solution:

This is one of De Morgan's laws, which states that the complement of the intersection of two sets is equal to the union of their complements.

Correct Answer: False

Solution:

The set of all integers is infinite because there is no limit to the number of integers.

Correct Answer: False

Solution:

The difference

A - B

is the set of elements that are in

A

but not in

B

, whereas

B - A

is the set of elements that are in

B

but not in

Solution:

Disjoint sets have no elements in common. Therefore, their intersection is the empty set.

Sets

AI Learning Assistant

Summary

Chapter Summary: Sets

Introduction

Basic Definitions

Set Operations

Important Laws

Venn Diagrams

Examples of Sets

Historical Note

Learning Objectives

Learning Objectives

Detailed Notes

Chapter 1: Sets

1.1 Introduction

1.2 Sets and their Representations

1.3 The Empty Set

1.6 Subsets

1.7 Universal Set

1.8 Venn Diagrams

1.9 Operations on Sets

Summary

Exam Tips & Common Mistakes

Common Mistakes and Exam Tips

Common Pitfalls

Tips for Success

Practice & Assessment

Multiple Choice Questions

Q1.What is the intersection of the sets A={1,3,5}A = \{1, 3, 5\}A={1,3,5} and B={3,4,5}B = \{3, 4, 5\}B={3,4,5}?

Correct Answer: B

Q2.If A={1,2,3}A = \{1, 2, 3\}A={1,2,3} and B={3,4,5}B = \{3, 4, 5\}B={3,4,5}, what is A∪BA \cup BA∪B?

Correct Answer: A

Q3.Which of the following sets is the solution to the inequality x2≤4x^2 \leq 4x2≤4?

Correct Answer: A

Q4.If A={1,2,3,4}A = \{1, 2, 3, 4\}A={1,2,3,4} and B={3,4,5,6}B = \{3, 4, 5, 6\}B={3,4,5,6}, what is A−BA - BA−B?

Correct Answer: A

Q5.If A={x:x is a vowel in the word ’EDUCATION’}A = \{x : x \text{ is a vowel in the word 'EDUCATION'}\}A={x:x is a vowel in the word ’EDUCATION’}, what is the set AAA?

Correct Answer: A

Q6.Given sets A={2,4,6,8,10}A = \{2, 4, 6, 8, 10\}A={2,4,6,8,10} and B={3,6,9,12}B = \{3, 6, 9, 12\}B={3,6,9,12}, what is A∪BA \cup BA∪B?

Correct Answer: D

Q7.If A={1,3,5,7,9}A = \{1, 3, 5, 7, 9\}A={1,3,5,7,9} and B={2,4,6,8,10}B = \{2, 4, 6, 8, 10\}B={2,4,6,8,10}, what is A∪BA \cup BA∪B?

Correct Answer: A

Q8.If A={x:x is a letter in the word ’TRIGONOMETRY’}A = \{x : x \text{ is a letter in the word 'TRIGONOMETRY'}\}A={x:x is a letter in the word ’TRIGONOMETRY’}, what is the set AAA?

Correct Answer: A

Q9.If A={2,4,6,8}A = \{2, 4, 6, 8\}A={2,4,6,8} and B={4,8,12}B = \{4, 8, 12\}B={4,8,12}, what is A∩BA \cap BA∩B?

Correct Answer: B

Q10.Which of the following sets represents the solution to the equation x2−5x+6=0x^2 - 5x + 6 = 0x2−5x+6=0?

Correct Answer: A

Q11.Which of the following is a subset of the set B={2,4,6,8}B = \{2, 4, 6, 8\}B={2,4,6,8}?

Correct Answer: A

Correct Answer: A

Q13.Which of the following is the complement of the set A={1,3,5,7,9}A = \{1, 3, 5, 7, 9\}A={1,3,5,7,9} with respect to the universal set U={1,2,3,4,5,6,7,8,9,10}U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}U={1,2,3,4,5,6,7,8,9,10}?

Correct Answer: A

Q14.If A={x:x is a student of Class XI presently studying in a school}A = \{x : x \text{ is a student of Class XI presently studying in a school}\}A={x:x is a student of Class XI presently studying in a school}, which of the following statements is true?

Correct Answer: A

Q15.Which of the following sets is a subset of B={2,4,6,8,10}B = \{2, 4, 6, 8, 10\}B={2,4,6,8,10}?

Correct Answer: B

Q16.Which of the following pairs of sets are disjoint?

Correct Answer: A

Q17.Which of the following represents the set B={x:x is an even natural number less than 10}B = \{x : x \text{ is an even natural number less than 10}\}B={x:x is an even natural number less than 10}?

Correct Answer: A

Q18.If A={x:x is a letter in the word ’MATHEMATICS’}A = \{x : x \text{ is a letter in the word 'MATHEMATICS'}\}A={x:x is a letter in the word ’MATHEMATICS’}, what is the set AAA?

Correct Answer: A

Q19.Which of the following pairs of sets are disjoint?

Correct Answer: D

Q20.Which of the following statements is true about the set A={x:x is a letter in the word ’MATHEMATICS’}A = \{x : x \text{ is a letter in the word 'MATHEMATICS'}\}A={x:x is a letter in the word ’MATHEMATICS’}?

Correct Answer: A

Q21.Which of the following sets is the complement of A={2,3,5}A = \{2, 3, 5\}A={2,3,5} with respect to the universal set U={1,2,3,4,5,6}U = \{1, 2, 3, 4, 5, 6\}U={1,2,3,4,5,6}?

Correct Answer: A

Q22.If A={x:x is a multiple of 3 and x≤15}A = \{x : x \text{ is a multiple of 3 and } x \leq 15\}A={x:x is a multiple of 3 and x≤15} and B={x:x is a multiple of 5 and x≤15}B = \{x : x \text{ is a multiple of 5 and } x \leq 15\}B={x:x is a multiple of 5 and x≤15}, what is A∪BA \cup BA∪B?

Correct Answer: A

Q23.Which of the following represents the set C={x:x is a natural number less than 6}C = \{x : x \text{ is a natural number less than 6}\}C={x:x is a natural number less than 6}?

Correct Answer: A

Q24.If A={x:x is a multiple of 4 and x≤20}A = \{x : x \text{ is a multiple of 4 and } x \leq 20\}A={x:x is a multiple of 4 and x≤20} and B={x:x is a multiple of 5 and x≤20}B = \{x : x \text{ is a multiple of 5 and } x \leq 20\}B={x:x is a multiple of 5 and x≤20}, what is A∪BA \cup BA∪B?

Correct Answer: A

Q25.Which of the following sets is finite?

Correct Answer: C

Q26.Which of the following is a well-defined set?

Correct Answer: B