Introduction to Sets – Class 11 Maths
A simple, clear guide to start Chapter 1: Sets
Understanding Sets is the first step in Class 11 Maths. This chapter builds the base for topics like Relations, Functions, Probability, and Calculus. If you’re beginning Class 11 or looking for structured learning, this guide explains the basics in the simplest way.
1. What is a Set?
A set is a well-defined collection of objects. “Well-defined” means anyone reading it should clearly know what belongs to it.
Examples:
A = {2, 4, 6, 8}
B = {red, blue, green}
The objects inside a set are called elements.
2. Ways to Write Sets
a) Roster Form
You list all elements one by one.
Example: P = {1, 3, 5, 7}
b) Set Builder Form
You describe the rule behind the elements.
Example: P = {x | x is an odd natural number less than 8}
Roster = list. Set Builder = rule.
3. Types of Sets
1. Empty Set
A set with no elements. Example: { }
2. Finite Set
A set with a fixed number of elements. Example: {a, b, c}
3. Infinite Set
A set with unlimited elements. Example: {1, 2, 3, 4, …}
4. Equal Sets
Two sets are equal if they have the same elements.
5. Subset
A is a subset of B if every element of A is inside B.
Example: {2, 4} is a subset of {1, 2, 3, 4}
4. Why Sets Are Important in Class 11
This chapter forms the base for:
- Relations & Functions
- Venn Diagrams
- Probability
- Logic & Counting
- Calculus (Class 12)
Students who learn Sets properly find later chapters much easier.
5. Video Lecture: Introduction to Sets
Watch the full explanation here:
6. Quick Revision Notes
Set: A collection of well-defined objects.
Element:
If a belongs to A → a ∈ A
If a does not belong to A → a ∉ A
Common Sets in Maths:
- N = Natural numbers
- W = Whole numbers
- Z = Integers
- Q = Rational numbers
- R = Real numbers
Important:
- Order of elements does not matter
- Repetition is ignored in sets
- {1, 2, 3} is the same as {3, 2, 1} and {1, 2, 2, 3}
7. Practice Questions (With Answers)
Q1: Write the roster form of the set of vowels.
Answer: {a, e, i, o, u}
Q2: Is {3, 5} a subset of {1, 3, 5, 7}?
Answer: Yes.
Q3: Identify the type of set: { }
Answer: Empty set.
Q4: Write the set-builder form of {2, 4, 6, 8}.
Answer: {x | x is an even natural number less than 10}
Q5: Which sets are equal?
A = {1, 2, 3}
B = {3, 1, 2}
Answer: A and B are equal sets.
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