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Relations and Functions

NCERT Class 11 Mathematics Chapter 2

Relations and Functions for Class 11 Maths and JEE: Cartesian product, relations, functions, domain and range, graphs and the algebra of real functions.

3 topics Updated 8 Nov 2026

For: Class 11 and JEE

In the syllabus: JEE Class 11 syllabus

With your textbook

NCERT Mathematics (Class 11), Chapter 2 “Relations and Functions”, reprint 2026-27.

Open the official NCERT chapter (PDF, 2.0 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Cartesian product of sets

    Ordered pairs, n(A × B) = pq, why A × B ≠ B × A, A × ϕ, R × R, laws with ∪ and ∩, and solved examples.

    NCERT Section 2.2 17 min read 5 solved examples 9 practice questions

  2. Relations

    Relations as subsets of A × B, arrow diagrams, domain, codomain and range, and the number of relations, 2 to the power pq.

    NCERT Section 2.3 15 min read 5 solved examples 9 practice questions

  3. Functions

    Function vs relation, domain and range, graphs of the modulus, signum and greatest integer functions, and solved examples.

    NCERT Section 2.4 22 min read 7 solved examples 10 practice questions

Key formulas in this chapter

Cartesian product

  • A × B = {(a, b): a ∈ A, b ∈ B}
  • (a, b) = (x, y) ⇔ a = x and b = y
  • n(A × B) = n(A) × n(B); A × ϕ = ϕ
  • A × (B ∩ C) = (A × B) ∩ (A × C)
  • A × (B ∪ C) = (A × B) ∪ (A × C)

Relations

  • R ⊂ A × B
  • domain of R = {x ∈ A: (x, y) ∈ R for some y ∈ B}
  • range of R = {y ∈ B: (x, y) ∈ R for some x ∈ A} ⊂ codomain B
  • number of relations from A to B = 2pq, where n(A) = p and n(B) = q

Functions

  • f: A → B, f(a) = b: one image for each a ∈ A
  • (f ± g)(x) = f(x) ± g(x); (fg)(x) = f(x) g(x)
  • (αf)(x) = α f(x)
  • (f/g)(x) = f(x)/g(x), where g(x) ≠ 0
  • |x| = x for x ≥ 0 and −x for x < 0
  • greatest integer: [x] = n, the integer with n ≤ x < n + 1

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