Skip to main content
Super TutorResources
Chapter 1 of 5
Revision Notes

Sets — Revision Notes

Punjab Board · Class 11 · Mathematics

Sets revision notes for Punjab Board Class 11 Mathematics: 4 topics in quick points. Key terms: A set is a well, In roster form and In set.

45 questions25 flashcards2 formulas & key relations5 concepts

Interactive on Super Tutor

Studying Sets? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for revision notes and more.

Try Super Tutor — Free

Free trial, no card needed.

A comparison illustrating how the same set can be represented using the Roster (listing) method and the Set-Builder method, with clear examples.
Super Tutor

Learn better with visuals Super Tutor pairs illustrations like this with notes and quizzes for Sets.

Key Topics to Revise

1

1. Sets and Their Representations

  • A set is a WELL-DEFINED collection of objects. The objects are called elements or members.
  • Sets are denoted by CAPITAL letters: A, B, C, X, Y, Z, etc.
  • Elements are denoted by SMALL letters: a, b, c, x, y, z, etc.
2

2. Types of Sets

  • EMPTY SET (Null Set / Void Set): A set with NO elements. Denoted by φ or {}. Example: {x : x is a natural number between 1 and 2} = φ.
  • Note: φ ≠ {0}. The set {0} has one element (zero), but φ has no elements.
  • FINITE SET: A set with a definite (countable) number of elements, including the empty set. Example: {1,2,3,4,5} is finite with n(A)=5.
3

3. Subsets, Supersets, and Power Set

  • SUBSET: A is a subset of B (written A ⊂ B) if EVERY element of A is also an element of B.
  • A ⊂ B means: if a ∈ A, then a ∈ B (using implication ⇒).
  • EVERY SET IS A SUBSET OF ITSELF: A ⊂ A for all sets A.
4

4. Intervals as Subsets of Real Numbers

  • For a, b ∈ R and a < b, there are four types of intervals:
  • OPEN INTERVAL (a, b) = {x : a < x < b} — both endpoints EXCLUDED.
  • CLOSED INTERVAL [a, b] = {x : a ≤ x ≤ b} — both endpoints INCLUDED.

Get complete notes with diagrams and examples

Full Notes

Key Concepts

A set is a wellIn roster formIn setThe empty set (denoted φA finite set has a definite

Frequently Asked Questions

What are the important topics in Sets for Punjab Board Class 11 Mathematics?
Key topics in Sets include Sets and Their Representations, Types of Sets, Subsets, Supersets, and Power Set, Intervals as Subsets of Real Numbers. Study these first, then practise questions on each for Class 11 exams.
How should I revise Sets for Class 11 exams?
Learn the core ideas first, then work through the 45 practice questions on Sets. 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 Sets

All Punjab Board Class 11 Mathematics Revision Notes

For serious students

Get the full Sets chapter — start free.

Quizzes, flashcards, an AI doubt solver and a study plan for Punjab Board Class 11 Mathematics. Free to start, no card needed.

Try Super Tutor Free
Try this chapter free