Sets is one of the most important foundation chapters in Mathematics (JKBOSE Class 10/11 syllabus).
It is not only a board exam topic, but also appears in competitive exams like JKSSB (FAA, Junior Assistant, Patwari, Police, Class-IV, etc.) under Quantitative Aptitude and Reasoning.
If you understand Sets properly, many later topics (Relations, Functions, Probability, Venn Diagrams, Reasoning) become easy.
This guide explains the entire chapter in a simple + revision-friendly format with examples and exam tips.
1. What is a Set? (Definition)
A set is a well-defined collection of distinct objects.
- Well-defined → Clear rule to decide membership
- Distinct → No repetition allowed
- Objects → called elements or members
Valid Examples
-
Prime numbers less than 20
{2, 3, 5, 7, 11, 13, 17, 19} -
Factors of 20
{1, 2, 4, 5, 10, 20} -
Even numbers less than 10
{2, 4, 6, 8}
Not a Set (Invalid)
- Good students in class
- Beautiful flowers
- Tall boys
Why?
Because they depend on opinion → not well-defined.
📌 Exam Rule:
If the statement is subjective → NOT a set
2. Notation & Membership
- Sets are written using capital letters (A, B, C…)
- Elements are written inside curly brackets { }
Symbols
| Symbol | Meaning |
|---|---|
| ∈ | belongs to |
| ∉ | does not belong to |
Example
A = {1, 2, 3, 4}
2 ∈ A
5 ∉ A
Number of elements → Cardinality
n(A) = 4
3. Representation of Sets (3 Methods)
| Method | Description | Example |
|---|---|---|
| Roster/Tabular | List all elements | A = {1,2,3,4} |
| Set-Builder | Rule/property form | A = {x : x is even < 10} |
| Venn Diagram | Pictorial circle representation | Used for union/intersection |
Important Rules
- Order does NOT matter → {1,2,3} = {3,2,1}
- Repetition not allowed → {1,2,2,3} = {1,2,3}
- Infinite sets → use set-builder form
4. Important Concepts to Remember
- Sets must be well-defined
- No repeated elements
- Order does not matter
- Empty set is still a valid set
- Infinite sets cannot be fully listed
5. Types of Sets (Very Important)
| Type | Meaning | Example |
|---|---|---|
| Empty Set | No elements | ∅ |
| Singleton | One element | {5} |
| Finite | Limited elements | {days of week} |
| Infinite | Unlimited elements | Natural numbers |
Empty Set
Symbol: ∅ or { }
Example:
Set of men with 4 legs → ∅
Singleton Set
Exactly one element
Example: {Sunday}
Finite Set
Can count elements
Example: {1,2,3}
Infinite Set
Unlimited elements
Example: {2,4,6,8,…}
Quick Revision Box
- Empty set → no elements
- Singleton → one element
- Finite → countable
- Infinite → endless
- Repetition not allowed
- Order irrelevant
FAQs (Quick Revision)
Q1. What is a set?
A well-defined collection of distinct objects.
Q2. Why is “good students” not a set?
Opinion-based → not well-defined.
Q3. Which form is used for infinite sets?
Set-builder form.
Q4. Is {1,2,2,3} a set?
No repetition allowed → becomes {1,2,3}.
Q5. What is an empty set?
A set with no elements.
JKSSB / Competitive Exam PYQs
-
Which is a well-defined set?
(a) Good students
(b) Prime numbers < 20 ✔
(c) Beautiful flowers
(d) Tall boys -
Even natural numbers form:
Finite / Infinite ✔ -
{x : x is day of week} is:
Finite ✔ -
Which is NOT a set?
Amazing actors ✔ -
Cardinality of {1,2,3,4}?
4 ✔ -
Empty set symbol?
∅ ✔ -
Set-builder of {2,4,6,8}?
{x : x is even < 10} ✔
Exam Tip (Very Important)
From Sets chapter, 4–5 marks are almost guaranteed in JKSSB exams.
Just remember:
- Definition
- Types of sets
- Symbols (∈, ∉, ∅)
- Roster vs Set-builder
This is one of the easiest scoring chapters in Maths + Reasoning.