# Sets Notes, Class 11 Mathematics | SwaVid

Sets: NCERT Class 11 Mathematics notes with key ideas, formulas, common mistakes and 3 quick checks with worked answers. Written by SwaVid from the textbook.

Canonical: https://www.swavid.com/cbse/class-11/maths/chapter/sets

Source: https://www.swavid.com/cbse/class-11/maths/chapter/sets

# Sets

## Formulas and definitions

## Key ideas

## Common mistakes

## Quick checks

## Keep going

## Questions parents ask

## Class 11 Mathematics on SwaVid

### Definition and representation of sets

### Empty, finite, and infinite sets

### Subsets and intervals of real numbers

### Universal set

### Venn diagrams and set operations

### Complement of a set

### Next chapter

### Related chapter

### All chapters

SwaVid › CBSE › Class 11 › Mathematics › Sets

Notes written by SwaVid from the NCERT textbook.

Class 11 Mathematics, Chapter 1. Key ideas, formulas and common mistakes.

CBSE does not print marks for a single chapter.

Short answer. This chapter introduces sets, their representations, subsets, intervals, and universal sets. Students learn how to represent sets using Venn diagrams and perform operations such as union, intersection, and complement.

Source: NCERT Mathematics (Reprint 2026-27) , Chapter 1, Sets

A set is a well-defined collection of objects. Sets are described in roster form by listing elements inside braces separated by commas, or in set-builder form by stating the defining property common to all elements.

An empty set contains no elements and is denoted by ∅ or {}. A set is finite if it consists of a specific number of elements; otherwise, it is infinite. Two sets A and B are equal if they have exactly the same elements.

A set A is a subset of B if every element of A is also in B. Subsets of real numbers can be represented as open intervals (a, b), closed intervals [a, b], or semi-open intervals.

A universal set U is a basic set that contains all objects or elements under discussion in a particular context. All other sets in that context are subsets of the universal set.

Venn diagrams represent sets as circles inside a rectangle that represents the universal set. The union of A and B contains elements in A or B or both, while the intersection contains elements belonging to both A and B.

The complement of a subset A with respect to universal set U is the set of all elements of U that are not in A, denoted by A′. De Morgan's laws state that (A ∪ B)′ = A′ ∩ B′ and (A ∩ B)′ = A′ ∪ B′.

Try each question first. Then tap it to see the answer.

The square bracket at -2 means it is included, so we use ≤.

The parenthesis at 3 means it is excluded, so we use <.

The set contains all real numbers x satisfying these conditions.

{x : x ∈ R, -2 ≤ x < 3}

Find A ∪ B by taking all elements in A or B: A ∪ B = {2, 3, 4, 5}

Take the complement with respect to U: (A ∪ B)′ = U - {2, 3, 4, 5}

(A ∪ B)′ = {1, 6}

{1, 6}

A - B contains elements in A that are not in B: {1, 3, 5}

B - A contains elements in B that are not in A: {6}

A - B = {1, 3, 5}, B - A = {6}

Relations and Functions .

Probability .

The 14 chapters of Class 11 Mathematics .

The CBSE Class 11 Maths curriculum says it gives no chapter or unit-wise weightage. Theory is 80 marks, plus 20 for internal assessment.

No. They are written by SwaVid from the NCERT textbook. The CBSE curriculum is the reference for what is assessed.

Relations and Functions.

SwaVid is an AI tutor for Indian students in Classes 6 to 12. It finds the earlier ideas a child missed, then teaches today’s chapter. Start free to see how it works.

- Ch 1 NCERT book
- 80 marks, theory paper
- 3 quick checks
- Writing the empty set as {∅} . Represent the empty set as ∅ or {}, without putting ∅ inside braces. The set {∅} is not empty because it contains one element, namely ∅.
- Confusing the symbols ∈ (element of) and ⊂ (subset of) . Use ∈ between an element and a set, such as 2 ∈ {2, 3}. Use ⊂ between two sets, such as {2} ⊂ {2, 3}.
- Mixing up open and closed interval brackets . Use square brackets [ ] when the endpoints are included, and round parentheses ( ) when the endpoints are excluded.

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