Sets Class 11 Formulas: Complete Formula List, Symbols & Types with Free PDF Download (JEE & Boards)
Sets Class 11 Maths Formula Sheet — Competishun
Sets Class 11 Formulas: Complete Formula List, Symbols & Types with Free PDF Download (JEE & Boards)
Sets is the very first chapter of Class 11 Maths, and for good reason. It is the foundation for relations and functions, probability and much of higher mathematics. Get your set formulas, symbols and types clear here, and the rest of the syllabus becomes far easier.
This page gives you the complete Sets Class 11 formula list in one place, all formulas, symbols, types of sets, set operations and Venn diagram formulas, written cleanly for quick revision. Download the free PDF below and keep it handy for boards and JEE.
Download the Sets Class 11 Formula Sheet PDF
Get all Sets formulas, symbols, types and Venn diagram formulas in one clean PDF, free. Perfect for last-minute revision before boards and JEE.
Download Free PDFWhat is a Set?
A set is a well-defined collection of distinct objects, called elements. "Well-defined" means it is always clear whether an object belongs to the set or not. Sets are written using capital letters, and elements inside curly braces.
Here is what this formula sheet covers:
Sets Symbols (Notation)
Knowing the symbols is half the chapter. Here are the essential ones.
| Symbol | Meaning |
|---|---|
| ∈ | belongs to (is an element of) |
| ∉ | does not belong to |
| ∅ or { } | empty set / null set |
| ⊂ | is a proper subset of |
| ⊆ | is a subset of |
| ⊄ | is not a subset of |
| ∪ | union |
| ∩ | intersection |
| A' | complement of set A |
| n(A) | cardinal number (number of elements) of A |
| U | universal set |
| P(A) | power set of A |
| Master these symbols first, every set formula is written using them. | |
Types of Sets
| Type | Definition |
|---|---|
| Empty / Null Set | A set with no elements, written ∅ or { } |
| Singleton Set | A set with exactly one element |
| Finite Set | A set with a countable, limited number of elements |
| Infinite Set | A set with unlimited elements |
| Equal Sets | Two sets with exactly the same elements: A = B |
| Equivalent Sets | Two sets with the same number of elements: n(A) = n(B) |
| Subset | A ⊆ B if every element of A is in B |
| Proper Subset | A ⊂ B if A ⊆ B and A ≠ B |
| Universal Set (U) | The set containing all elements under consideration |
| Power Set P(A) | The set of all subsets of A |
| The empty set is a subset of every set, and every set is a subset of itself. | |
Set Operations
| Operation | Definition |
|---|---|
| Union (A ∪ B) | all elements in A or B or both |
| Intersection (A ∩ B) | elements common to both A and B |
| Difference (A − B) | elements in A but not in B = A ∩ B' |
| Complement (A') | A' = U − A (all elements not in A) |
| Symmetric Difference | A Δ B = (A − B) ∪ (B − A) |
| Disjoint Sets | A ∩ B = ∅ (no common elements) |
| Difference A − B is not the same as B − A. Order matters in the difference operation. | |
Key Cardinality Formulas (Most Important)
These are the formulas that appear most in exams and JEE. Memorise them.
| Formula | Expression |
|---|---|
| Union of 2 sets | n(A∪B) = n(A) + n(B) − n(A∩B) |
| Disjoint sets | n(A∪B) = n(A) + n(B), if A∩B = ∅ |
| Union of 3 sets | n(A∪B∪C) = n(A) + n(B) + n(C) − n(A∩B) − n(B∩C) − n(C∩A) + n(A∩B∩C) |
| Only A | n(only A) = n(A) − n(A∩B) |
| Number of subsets | 2ⁿ (n = number of elements) |
| Number of proper subsets | 2ⁿ − 1 |
| Elements in power set | n(P(A)) = 2ⁿ |
| Complement count | n(A') = n(U) − n(A) |
| The n(A∪B) and n(A∪B∪C) formulas are the most commonly tested. Practise Venn diagram word problems using them. | |
Algebra of Sets (Laws & Properties)
| Law | Formula |
|---|---|
| Commutative | A∪B = B∪A | A∩B = B∩A |
| Associative | (A∪B)∪C = A∪(B∪C) |
| Distributive | A∪(B∩C) = (A∪B)∩(A∪C) |
| Distributive | A∩(B∪C) = (A∩B)∪(A∩C) |
| Identity | A∪∅ = A | A∩U = A |
| Idempotent | A∪A = A | A∩A = A |
| De Morgan's Law 1 | (A∪B)' = A' ∩ B' |
| De Morgan's Law 2 | (A∩B)' = A' ∪ B' |
| Complement laws | A∪A' = U | A∩A' = ∅ |
| De Morgan's laws are a favourite in JEE. Learn them cold, they simplify many problems instantly. | |
Why Sets Matters for JEE and Boards
- Foundation chapter: Relations, functions and probability all build on sets
- Easy scoring: Direct formula-based questions make it a high-return topic
- Venn diagram problems: The n(A∪B∪C) formula solves many word problems fast
- Quick revision: Small chapter, big payoff when revised from a formula sheet
How to Use This Formula Sheet
- Learn the symbols first: Everything else depends on them
- Focus on cardinality formulas: n(A∪B) and n(A∪B∪C) are most tested
- Practise Venn diagrams: Convert word problems into set formulas
- Revise before exams: Skim the PDF the night before your test
Get the Complete Sets Formula Sheet PDF Free
Download the full Sets Class 11 formula sheet and revise anytime, anywhere.
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Frequently Asked Questions — Sets Class 11 Formulas
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