Menu

Sets

NCERT Class 11 Mathematics Chapter 1

Sets for Class 11 Maths and JEE: roster and set-builder form, types of sets, subsets, power set, Venn diagrams, union, intersection, De Morgan’s laws.

10 topics Updated 8 Nov 2026

For: Class 11 and JEE, unless a topic says otherwise

In the syllabus: JEE Class 11 syllabus

With your textbook

NCERT Mathematics (Class 11), Chapter 1 “Sets”, reprint 2026-27.

Open the official NCERT chapter (PDF, 2.2 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Sets and their representations

    Roster form and set-builder form for Class 11 Maths and JEE: what a set is, the sets N, Z, Q, R, converting between the forms, with solved examples.

    NCERT Section 1.2 15 min read 5 solved examples 12 practice questions

  2. The empty set

    The empty set for Class 11 Maths and JEE: what the null or void set is, its symbols, how to spot one, and why ϕ, {0} and {ϕ} are different.

    NCERT Section 1.3 8 min read 3 solved examples 7 practice questions

  3. Finite and infinite sets

    Finite and infinite sets for Class 11 Maths and JEE: how to tell them apart, n(S) and the cardinal number, roster form with dots, and solved examples.

    NCERT Section 1.4 8 min read 3 solved examples 7 practice questions

  4. Equal sets

    Equal sets for Class 11 Maths and JEE: when two sets are equal, why order and repetition do not matter, equal vs equivalent sets, and solved examples.

    NCERT Section 1.5 9 min read 4 solved examples 7 practice questions

  5. Subsets

    Proper subsets and supersets, ∈ against ⊂, the symbol ⊆, and open, closed and half-open intervals, with solved examples.

    NCERT Section 1.6 15 min read 4 solved examples 12 practice questions

  6. Power set

    Power set for JEE Main: what P(A) is, how to list it, the formula n[P(A)] = 2 and why it holds, proper subsets and P(ϕ), with solved examples.

    JEE only 9 min read 4 solved examples 9 practice questions

  7. Universal set

    The universal set for Class 11 Maths and JEE: a set containing every element needed in a problem, how to choose it, and why the choice matters.

    NCERT Section 1.7 7 min read 3 solved examples 5 practice questions

  8. Venn diagrams

    Venn diagrams for Class 11 Maths and JEE: the universal set as a rectangle, sets as circles, subsets, disjoint and overlapping sets, with examples.

    NCERT Section 1.8 8 min read 3 solved examples 5 practice questions

  9. Operations on sets

    Union, intersection, difference, disjoint sets, the laws of algebra of sets and n(A ∪ B), with solved examples.

    NCERT Section 1.9 16 min read 5 solved examples 11 practice questions

  10. Complement of a set

    The complement of a set for Class 11 Maths and JEE: A′ as U − A, the complement laws and De Morgan’s laws, with Venn diagrams and examples.

    NCERT Section 1.10 12 min read 4 solved examples 9 practice questions

Key formulas in this chapter

Sets and their representations

  • a ∈ A: a belongs to A; b ∉ A: b does not belong to A
  • Roster form: {1, 2, 3, 6} (order irrelevant, no repetition)
  • Set-builder form: {x: x has property P}, read “the set of all x such that x has property P”

The empty set

  • Empty set: ϕ = { }, with n(ϕ) = 0
  • {0} and {ϕ} are not empty: each has 1 element

Finite and infinite sets

  • n(S) = number of distinct elements of a finite set S; n(ϕ) = 0
  • Finite: n(S) = 0, 1, 2, …; otherwise infinite

Equal sets

  • A = B ⇔ (every element of A is in B) and (every element of B is in A)
  • {1, 2, 3} = {3, 1, 2} = {1, 1, 2, 3}

Subsets

  • A ⊂ B ⇔ (a ∈ A ⇒ a ∈ B); A ⊂ B and B ⊂ A ⇔ A = B
  • (a, b) = {x: a < x < b}; [a, b] = {x: a ≤ x ≤ b}
  • [a, b) = {x: a ≤ x < b}; (a, b] = {x: a < x ≤ b}; length b − a
  • A set with n elements has 2n subsets

Power set

  • P(A) = {S: S ⊂ A}
  • n[P(A)] = 2n when n(A) = n
  • Proper subsets: 2n − 1; non-empty proper subsets: 2n − 2 for n ≥ 1, and 0 for n = 0

Universal set

  • A ⊂ U for each set A under discussion

Venn diagrams

  • U: rectangle; A, B, …: circles inside U
  • B ⊂ A: circle B inside circle A
  • A, B disjoint: circles drawn apart

Operations on sets

  • A ∪ B = {x: x ∈ A or x ∈ B}; A ∩ B = {x: x ∈ A and x ∈ B}
  • A − B = {x: x ∈ A and x ∉ B}
  • A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C); A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
  • n(A ∪ B) = n(A) + n(B) − n(A ∩ B)

Complement of a set

  • A′ = {x: x ∈ U and x ∉ A} = U − A
  • A ∪ A′ = U; A ∩ A′ = ϕ; (A′)′ = A; ϕ′ = U; U′ = ϕ
  • (A ∪ B)′ = A′ ∩ B′; (A ∩ B)′ = A′ ∪ B′

More in Mathematics