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Relations and Functions — Revision Notes

Punjab Board · Class 11 · Mathematics

Relations and Functions revision notes for Punjab Board Class 11 Mathematics: 4 topics in quick points. Includes Cartesian Product of Sets, Relations.

45 questions25 flashcards5 concepts

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Key Topics to Revise

1

Cartesian Product of Sets

  • The Cartesian Product of two non-empty sets P and Q, written as P × Q, is the set of ALL ordered pairs (p, q) where p belongs to P and q belongs to Q.
  • Order matters in ordered pairs: (a, b) ≠ (b, a) unless a = b.
  • Two ordered pairs (a, b) and (c, d) are equal if and only if a = c AND b = d.
2

Relations

  • A relation R from set A to set B is any SUBSET of A × B. So every relation is a collection of ordered pairs.
  • A relation can be represented in three ways: Roster form (list all pairs), Set-builder form (describe the rule), Arrow diagram.
  • The DOMAIN of R is the set of all FIRST elements of the ordered pairs in R.
3

Functions — Definition and Types

  • A function f from A to B (written f: A → B) is a SPECIAL relation where EVERY element of A has EXACTLY ONE image in B.
  • Two conditions must hold: (1) Every element of domain A must have an image. (2) No element of A can have more than one image.
  • If (a, b) ∈ f, we write f(a) = b. Here b is the IMAGE of a, and a is the PRE-IMAGE of b.
4

Algebra of Real Functions

  • You can combine two functions f and g defined on the same domain X ⊆ R using arithmetic operations.
  • Sum: (f + g)(x) = f(x) + g(x) for all x ∈ X
  • Difference: (f − g)(x) = f(x) − g(x) for all x ∈ X

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Key Concepts

The Cartesian product of two nonA relation R from setFor a relation R fromA function f from setFor a relation to be

Frequently Asked Questions

What are the important topics in Relations and Functions for Punjab Board Class 11 Mathematics?
Key topics in Relations and Functions include Cartesian Product of Sets, Relations, Functions — Definition and Types, Algebra of Real Functions. Study these first, then practise questions on each for Class 11 exams.
How should I revise Relations and Functions for Class 11 exams?
Learn the core ideas first, then work through the 45 practice questions on Relations and Functions. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Relations and Functions

All Punjab Board Class 11 Mathematics Revision Notes

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