In mathematics, a set is a clear collection of different objects. Sets are the basis of modern math and are found in areas like algebra, logic, and probability. To help you understand this concept, we’ve put together a list of commonly asked questions about sets, along with answers and explanations. Whether you are a student encountering sets for the first time or reviewing for an exam, these questions and answers will help improve your understanding of sets.

Table of Contents

What Is a Set?
Types of Set Notations
Sets Questions with Answers
Common Types of Sets in Questions
Conclusion
FAQs On Sets Questions

What Is a Set?

A set is a group of well-defined and distinct objects. The items in a set are called elements or members.

Example:
A = {2, 4, 6, 8}
This is a set of even numbers less than 10.

Types of Set Notations

There are two common ways to write sets:

1. Roster Form

In roster form, the elements of a set are listed inside curly brackets {}.

Example:
Set of vowels in English:
A = {a, e, i, o, u}

2. Set-Builder Form

In set-builder form, a rule or condition is given to define the elements.

Example:
B = {x | x is a natural number less than 5}
This means: B = {1, 2, 3, 4}

Sets Questions with Answers

Here are some important questions on sets, ideal for students and competitive exam practice.

1. Write the solution set of the equation $y%5E%7B2%7D-9%3D0$ in roster form.

Solution: $y%5E%7B2%7D-9$ = $y%5E%7B2%7D-3%5E%7B2%7D$ = $(y%20%E2%80%93%203)(y%20%2B%203)$

y = 3, -3

Thus, solution set A = {-3, 3}

2. Find the union of P = {2, 4, 6, 8, 10} and Q = {1, 3, 5, 7, 9}?

Solution:

Set P = {2, 4, 6, 8, 10}

Set Q = {1, 3, 5, 7, 9}

To find the union of sets P and Q, we have to write all elements P and Q together as:

P ∪ Q = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

3. Find the intersection of A = {1, 2, 3, 4, 5} and B = {2, 4, 6, 8, 10}?

Solution:

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

Set B = {2, 4, 6, 8, 10}

To find the intersection of sets A and B, we have to write all common elements from set A and B as:

A ∩ B = {2, 4}

4. If P = {2, 3, 4, 5, 6, 7, 8, 9} and Q = {2, 4, 8, 12, 16}, what is difference of sets: P − Q and Q − P?

Answer:

Set P = {2, 3, 4, 5, 6, 7, 8, 9}

Set Q = {2, 4, 8, 12, 16}

Difference between set P and Q:

P − Q = {3, 5, , 6, 7, 9}

Difference between set Q and P:

Q − P = {12, 16}

5. If set P = {2, 3, 4, 5, 8}, Q = {11, 10, 12}, and R = {1, 5, 6, 7, 9}, Find the universal set for all three sets?

Answer: Let U be the universal set for P, Q and R then U = Elements of Set A + Elements of Set B + Elements of Set C

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

6. Write the set A = {1, 3, 5, 7, 9} in set-builder form.

Solution: To write set in set-builder form follow the steps below:

Step 1: First, observe the pattern of elements in set A = {1, 3, 5, 7, 9} . They are odd natural numbers up to 10.

Step 2: Write the condition in set-builder form using variable x:

A = { x | x is an even natural number, 2 ≤ x ≤ 10 }

7. Find A $%5Ccup$ (B $%5Ccup$ C), if A = {2, 4, 6}, B = {1, 3, 5} and C = {7, 8, 9}.

Solution: To find A $%5Ccup$ (B $%5Ccup$ C) we first have to find (A $%5Ccup$ B) $%5Ccup$ (A $%5Ccup$ C)

(A $%5Ccup$ B) $%5Ccup$ (A $%5Ccup$ C) = {1, 2, 3, 4, 5, 6} $%5Ccup$ {2, 4, 6, 7, 8, 9}

A $%5Ccup$ (B $%5Ccup$ C) = {1, 2, 3, 4, 5, 6, 7, 8, 9}

Practice Questions on Sets

You can practice the following:

1. Write the set of prime numbers less than 10 in roster form.

Answer: P = {2, 3, 5, 7}

2. Write the set E = {2, 4, 6, 8, 10} in set-builder form.

Answer: A = {2, 4, 6, 8, 10}

So, in set-builder form of set is A = {x | x is an even natural number, x < 12}

3. Which of the following is an empty set?

a) Set of even numbers divisible by 5 and 2
b) Set of natural numbers less than 1
c) Set of vowels in the word "sky"

Answer:
Correct answer: b) Set of natural numbers less than 1
Because the smallest natural number is 1. So, the set is empty.

4. Is the set A = {1, 2, 3, …, 100} finite or infinite?

Answer:
It is a finite set because the number of elements is countable and limited.

5. Write the set of letters in the word “MATHS”.

Answer:
A = {M, A, T, H, S}
Each element appears only once because sets do not allow repetition.

6. Which of the following sets are infinite?

a) Set of natural numbers
b) Set of vowels in English
c) Set of odd numbers greater than 10

Answer:
a) and c) are infinite sets because they go on forever.

7. Write the set of first 5 odd numbers.

Answer:
O = {1, 3, 5, 7, 9}

8. Represent the set A = {2, 4, 6, 8} in set-builder form.

Answer:
A = {x | x is an even number, 1 < x < 10}

9. Which of the following is a finite set?

Set of months in a year
Answer:
Yes, it is finite. There are only 12 months in a year.

10. What is the cardinality of the set A = {3, 6, 9}?

Answer:
Cardinality means the number of elements in a set.
So, n(A) = 3

Common Types of Sets in Questions

Let’s review different types of sets that often appear in questions:

Empty Set: No elements (e.g., { })
Finite Set: Limited number of elements
Infinite Set: Unlimited elements
Equal Sets: Have exactly the same elements
Equivalent Sets: Have the same number of elements (even if different items)
Subset: A set whose elements all belong to another set
Universal Set: Contains all elements under consideration
Power Set: Set of all subsets of a given set

Conclusion

Practising set questions regularly helps students build a strong foundation in mathematics. Whether it's understanding the difference between roster and set-builder form or identifying finite and infinite sets, these questions make learning straightforward and efficient. This blog covered the most common questions on sets, along with clear questions and answers, to support your learning. It's perfect for students, competitive exam takers, or anyone revisiting basic math.

Frequently Asked Questions On Sets Questions

1. What is a set?

Answer: A set is a collection of distinct objects. These objects are called elements. Sets are usually written using curly brackets, e.g., A = {1, 2, 3}.

2. What is a roster form of a set?

Answer: In roster form, all elements of a set are listed inside curly brackets, separated by commas.

Example: Set of vowels: {a, e, i, o, u}

3. What is the set-builder form?

Answer: Set-builder form uses a rule or condition to define the elements of a set.

Example: A = {x | x is an even number less than 10}

4. What is an empty set?

Answer: An empty set has no elements. It is written as {} or ∅.

Example: The set of natural numbers less than 1 is an empty set.

5. What are finite and infinite sets?