Class 11 Maths NCERT Solutions Chapter 1 Sets | Boundless Maths
Chapter 1 Class 11 Maths NCERT Solutions · Unit I · Sets and Functions

Class 11 Maths NCERT Solutions Chapter 1: Sets

Free, step-by-step NCERT Solutions for all five exercises of this chapter — set representation, subsets and intervals, Venn diagrams, union, intersection, difference and complement — solved the way CBSE awards marks, with the key definitions and formulas right on this page.

6Exercises (incl. Misc.)
49Total Questions
2026-27CBSE Syllabus
100%Solved

Class 11 Maths NCERT Solutions Chapter 1 — Overview

A set is a well-defined collection of objects, written in roster or set-builder form. This chapter covers how sets are classified (empty, finite, infinite, equal), how they compare (subsets, intervals, universal set), and how they combine — union, intersection, difference and complement, with Venn diagrams as the visual anchor throughout and De Morgan's laws tying complement to union and intersection.

How the Chapter Builds

One Idea Leads to the Next

1

Sets & Representation

Roster form and set-builder form — the two ways to write down a set. Exercise 1.1.

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2

Empty, Finite, Infinite & Equal Sets

Sorting sets by size and comparing two sets for equality. Exercise 1.2.

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3

Subsets, Intervals & Universal Set

A ⊂ B, interval notation on R, and the universal set U everything sits inside. Exercise 1.3.

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4

Venn Diagrams & Operations

Union, intersection and difference — and how to see them in a picture. Exercise 1.4.

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5

Complement & De Morgan's Laws

A′ = U − A, and how complement distributes over union and intersection. Exercise 1.5.

Quick Reference

Important Formulas — Chapter 1

Everything you need before you start solving. This is a summary for quick recall — the Formula Cards below has the full printable version for all of Sets.

Sets and their Representation (§1.2)

Roster (tabular) form

A=\{2,4,6\}

Every element is listed once, separated by commas, order does not matter. Not practical for infinite or unpatterned sets.

Set-builder form

A=\{x : x \text{ is an even natural number}, x<7\}

Describes the property every element must satisfy — essential when elements can't all be listed.

Belongs to / does not belong to

a\in A \qquad b\notin A

ε (belongs to) relates an element to a set — never confuse it with ⊂, which relates a set to a set.

Subsets, Intervals & Universal Set (§1.6–1.7)

Subset

A\subset B \iff (a\in A \Rightarrow a\in B)

φ is a subset of every set, and every set is a subset of itself. A ⊂ B and B ⊂ A together give A = B.

Open & closed intervals

(a,b)=\{y : a

A round bracket excludes the endpoint, a square bracket includes it. [a, b) and (a, b] mix the two.

Universal set

U \supseteq A, B, C, \ldots

The basic set relevant to a particular context — every set under discussion is treated as a subset of U.

Operations on Sets (§1.9)

Union

A\cup B=\{x : x\in A \text{ or } x\in B\}

Everything in A, in B, or in both — common elements are written only once.

Intersection

A\cap B=\{x : x\in A \text{ and } x\in B\}

Only the elements common to both sets. A ∩ B = φ means A and B are disjoint.

Difference

A-B=\{x : x\in A \text{ and } x\notin B\}

Elements in A but not in B. In general A − B ≠ B − A, and A − B, A ∩ B, B − A are mutually disjoint.

Distributive law

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

∩ distributes over ∪, and equally, ∪ distributes over ∩ — provable directly from a Venn diagram.

Complement & De Morgan's Laws (§1.10)

Complement of a set

A'=\{x : x\in U \text{ and } x\notin A\}=U-A

A′ always depends on which universal set U has been fixed for the problem.

De Morgan's laws

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

The complement of a union is the intersection of the complements, and vice versa.

Complement laws

A\cup A'=U \qquad A\cap A'=\phi \qquad (A')'=A

Also φ′ = U and U′ = φ — worth memorising, since fill-in-the-blank questions target exactly these.

Decision Guide

Which Sets Concept Applies?

A quick way to decide, once you know what the question is actually asking for.

What the question is askingUse thisWhy
Rewrite a set from a description into a list, or vice versaRoster ⟷ set-builder conversionFind the common property (or list the members it produces) (§1.2).
Decide if two differently-written sets are actually the sameEqual sets testShow every element of A is in B and every element of B is in A (§1.5).
Decide if every element of one set lies inside anotherSubset testa ∈ A must force a ∈ B for every single a (§1.6).
Write an inequality on R using interval notationInterval notationMatch strict/non-strict inequalities to round/square brackets (§1.6.2).
Find elements that are in either set (or both)UnionCombine both sets, writing shared elements only once (§1.9.1).
Find elements common to both setsIntersectionKeep only what appears in every set involved (§1.9.2).
Find elements in one set but excluded from anotherDifference (A − B)Order matters — A − B and B − A are generally different sets (§1.9.3).
Find everything outside a set, within the universal setComplementA′ = U − A, so first pin down U (§1.10).
Simplify (A ∪ B)′ or (A ∩ B)′De Morgan's lawsSwap the operation and complement each set separately (§1.10).
Avoid These

Common Mistakes to Avoid in This Chapter

Drawn from where students actually lose marks across all five exercises.

  • Confusing ∈ (belongs to) with ⊂ (subset of) — ∈ relates an element to a set, ⊂ relates a set to a set. Writing {a} ∈ A instead of {a} ⊂ A (or a ∈ A) is one of the most common slips in this chapter.
  • Repeating elements, or reordering them, and thinking it changes the set — {1, 2, 3}, {2, 2, 1, 3, 3} and {3, 1, 2} are all the same set. Roster form order and repetition have no relevance.
  • Forgetting that φ is a subset of every set, including itself — this is used constantly when listing all subsets of a given set, and skipping it is a guaranteed lost mark.
  • Getting round vs. square brackets backwards in interval notation — a round bracket (or open circle on the number line) excludes the endpoint; a square bracket (filled circle) includes it. Double-check against the original inequality's ≤ or < before writing the interval.
  • Assuming A − B equals B − A — in general they don't. A − B keeps what's in A only, B − A keeps what's in B only; the two are disjoint from each other and from A ∩ B.
  • Applying De Morgan's laws without swapping the operation — (A ∪ B)′ becomes A′ ∩ B′, not A′ ∪ B′. Students often complement each set correctly but forget to flip ∪ to ∩ (or ∩ to ∪).
  • Forgetting the complement depends on the universal set U — the same set A can have different complements depending on what U has been fixed as for that problem; always check U before finding A′.
Solve Chapter-Wise

Class 11 Maths NCERT Solutions Chapter 1 — Choose an Exercise

1.1

Exercise 1.1

Sets and their representations — well-defined collections, roster form and set-builder form · 6 questions

Solve Exercise 1.1 →
1.2

Exercise 1.2

The empty set, finite and infinite sets, and equal sets · 6 questions

Solve Exercise 1.2 →
1.3

Exercise 1.3

Subsets, subsets of R, intervals as subsets of R, and the universal set · 8 questions

Solve Exercise 1.3 →
1.4

Exercise 1.4

Venn diagrams, union, intersection and difference of sets · 12 questions

Solve Exercise 1.4 →
1.5

Exercise 1.5

Complement of a set and De Morgan's laws · 7 questions

Solve Exercise 1.5 →
M

Miscellaneous Exercise

Proofs of subset and set-identity results, tying the whole chapter together · 10 questions

Solve Miscellaneous →

📐 Keep the Formulas Handy

Every formula for Sets — plus every other Class 11 Maths chapter — in one printable PDF.

Get Formula Cards →
Common Questions

Frequently Asked Questions

Quick answers from Class 11 Maths NCERT Solutions Chapter 1, Sets.

How many exercises are there in Chapter 1, Sets?
There are five main exercises — 1.1 (Sets and their Representations, 6 questions), 1.2 (Empty, Finite, Infinite and Equal Sets, 6 questions), 1.3 (Subsets, Intervals and Universal Set, 8 questions), 1.4 (Union, Intersection and Difference of Sets, 12 questions) and 1.5 (Complement of a Set, 7 questions) — plus a Miscellaneous Exercise of 10 questions covering proofs of set identities, totalling 49 questions.
What is the difference between roster form and set-builder form?
Roster form lists every element of a set individually inside braces, separated by commas, such as {1, 3, 5, 7, 9}. Set-builder form instead describes a common property shared by every element and no other object, written as {x : x has the property}. Roster form works well for small or clearly patterned sets, while set-builder form is essential for sets that cannot be listed out, such as the set of all real numbers satisfying an inequality.
Why is the empty set a subset of every set?
A set A is a subset of B if every element of A is also an element of B. The empty set has no elements at all, so there is no element of the empty set that could fail to belong to B — the condition is satisfied vacuously. This is why φ is a subset of every set, including itself.
What is the difference between A minus B and the complement of A?
A minus B is the set of elements that belong to A but not to B, and it can be found between any two sets. The complement of A is a special case of this idea — it is U minus A, where U is the universal set — so the complement always depends on which universal set has been fixed for the problem.
Where can I find the official NCERT textbook for this chapter?
Sets is Chapter 1 of the NCERT Class 11 Mathematics textbook, published by the National Council of Educational Research and Training (NCERT) and prescribed by CBSE. You can download the official textbook PDF directly from ncert.nic.in, NCERT's official website — the solutions on this page follow the exercises exactly as they appear there.
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