Class 11 Maths Sets Definitions, Types & Examples
The chapter Sets is the first and one of the most important chapters of Class 11 Mathematics. It introduces the basic language of mathematics that is used in almost every other chapter. Understanding sets clearly helps students learn relations, functions, probability, and many advanced topics easily.
π What is a Set?
A set is a well-defined collection of objects or elements.
The objects in a set are called elements.
Example:
- A set of natural numbers less than 5 = {1, 2, 3, 4}
- A set of vowels in English = {a, e, i, o, u}
βοΈ Representation of Sets
Sets can be represented in two ways:
- Roster Form
Elements are listed inside curly brackets.
Example: A = {2, 4, 6, 8} - Set-Builder Form
Elements are described by a property.
Example: A = {x | x is an even natural number}
π Types of Sets
- Empty Set: A set with no elements
- Singleton Set: A set with only one element
- Finite Set: A set with a limited number of elements
- Infinite Set: A set with unlimited elements
- Equal Sets: Sets having the same elements
- Subset: A set whose elements belong to another set
- Universal Set: A set containing all possible elements under discussion
π’ Operations on Sets
NCERT introduces basic operations on sets:
- Union (A βͺ B) β All elements of A and B
- Intersection (A β© B) β Common elements of A and B
- Difference (A β B) β Elements of A not in B
- Complement (Aβ²) β Elements not present in A
These operations are used widely in mathematics and probability.
π Venn Diagrams
Venn diagrams are visual representations of sets using circles.
They help in understanding:
- Union
- Intersection
- Difference
- Complement of sets
Venn diagrams make problem-solving easier and faster in exams.
π§ Important Symbols Used in Sets
- β : Belongs to
- β : Does not belong to
- β : Subset
- βͺ : Union
- β© : Intersection
- Γ : Empty set
- U : Universal set