NCERT Class 11 Mathematics Mathematics: Chapter 1 — SETS
This chapter introduces the fundamental concept of sets in mathematics, a cornerstone for various branches like relations, functions, geometry, and probability. Developed by German mathematician Georg Cantor, set theory provides a rigorous way to define collections of objects. The chapter defines a set as a well-defined collection where membership can be definitively determined. It introduces standard notations for number sets like natural numbers (N), integers (Z), rational numbers (Q), and real numbers (R). Key concepts include elements, membership (using the symbol ∈), and non-membership (∉). Two primary methods for representing sets are discussed: the Roster form, where elements are listed within braces, and the Set-builder form, which describes the properties of the elements. This foundational understanding of sets is crucial for further mathematical studies in Class 11 and beyond.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 11 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 1 — SETS |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 4 minutes |
| Word count | 697 |
Learning outcomes
- Define a set as a well-defined collection of objects.
- Understand and use standard notations for number sets (N, Z, Q, R).
- Distinguish between elements belonging to a set (∈) and those not belonging (∉).
- Represent sets using the Roster form.
- Understand the concept of Set-builder form for representing sets.
Vocabulary
| Word | Meaning |
|---|---|
| Set | A well-defined collection of objects. |
| Element | An object belonging to a set; also called a member. |
| ∈ | Symbol denoting 'belongs to' or 'is an element of'. |
| ∉ | Symbol denoting 'does not belong to' or 'is not an element of'. |
| Roster form | A method of representing a set by listing all its elements within braces. |
| Set-builder form | A method of representing a set by describing the properties of its elements. |
| Natural numbers (N) | The set of all positive integers: {1, 2, 3,...}. |
| Integers (Z) | The set of all whole numbers, positive, negative, and zero: {..., -2, -1, 0, 1, 2,...}. |
| Rational numbers (Q) | The set of all numbers that can be expressed as a fraction p/q, where p and q are integers and q ≠ 0. |
| Real numbers (R) | The set of all rational and irrational numbers. |
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Practice questions
- Which of the following collections are sets? (i) The collection of all months of a year beginning with the letter J. (ii) The collection of difficult problems in mathematics. Answer: (i) is a set because it is well-defined. (ii) is not a set because 'difficult' is subjective.
- Let A = {1, 3, 5, 7}. Which of the following statements are true? (i) 3 ∈ A (ii) 2 ∉ A Answer: Both statements (i) and (ii) are true.
- Write the set of all vowels in the English alphabet in roster form. Answer: {a, e, i, o, u}
- Write the set {2, 4, 6, 8} in set-builder form. Answer: {x: x is an even natural number less than 10}
Practice MCQs
Q1. Who developed the theory of sets?
Explanation: Georg Cantor is credited with developing the theory of sets in the late 19th century.
Q2. Which of the following is a well-defined collection?
Explanation: The collection of all natural numbers is well-defined as we can definitively determine if a number is natural or not.
Q3. The symbol '∈' denotes:
Explanation: The Greek symbol epsilon (∈) is used in set theory to indicate that an element belongs to a particular set.
Q4. Which set represents the odd natural numbers less than 10 in roster form?
Explanation: The odd natural numbers less than 10 are 1, 3, 5, 7, and 9. These are listed within braces in roster form.
Q5. The set of all integers is denoted by:
Explanation: The symbol Z is conventionally used to represent the set of all integers in mathematics.
Frequently asked questions
What is a set in mathematics?
A set is a well-defined collection of distinct objects, where we can definitively determine whether a given object belongs to the collection or not.
Who is considered the father of set theory?
Georg Cantor, a German mathematician, is credited with developing the theory of sets.
What are the two main ways to represent a set?
The two main ways are the Roster form (listing elements) and the Set-builder form (describing properties).
What does the symbol '∈' mean in set theory?
The symbol '∈' means 'belongs to' or 'is an element of'. For example, if a is an element of set A, we write a ∈ A.
What is the difference between roster form and set-builder form?
Roster form lists all elements within braces, like {1, 2, 3}. Set-builder form describes the elements by their properties, like {x: x is a natural number less than 4}.
What are the standard symbols for number sets?
N for natural numbers, Z for integers, Q for rational numbers, and R for real numbers.
Related resources
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Topics covered
NCERT Class 11 Mathematics — Mathematics — Chapter 1 — SETS. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.