Sets

Complete Class 11 Sets chapter with definitions, notation, types of sets, subsets, power set, Venn diagrams, set operations, algebra of sets, and applications.

1.What is a Set?
Clear and simple explanation of sets, their notation, elements, empty set, and basic types of sets with examples.
2.Set Notation & Symbols
Explanation of set notation, symbols, roster form, set-builder form, and common ways to represent elements in a set.
3.Roster Form & Set Builder Form
Clear explanation of roster form and set-builder form with rules, examples, and differences between the two ways of writing sets.
4.Cardinality of a Set
Explanation of cardinality of a set, meaning, notation, examples, and how to count elements in different types of sets.
5.Types of Sets (Overview)
Overview of different types of sets such as finite, infinite, equal, equivalent, singleton, and empty sets with simple examples.
6.Empty Set
Meaning of the empty set, notation, examples, and important points about sets with no elements.
7.Singleton Set
Meaning of a singleton set, notation, examples, and key points about sets with exactly one element.
8.Finite and Infinite Sets
Explanation of finite and infinite sets with meaning, examples, and simple ways to identify the size of a set.
9.Equal Sets
Meaning of equal sets, simple examples, and how to check whether two sets are equal.
10.Equivalent Sets
Meaning of equivalent sets with examples and simple ways to check if two sets have the same number of elements.
11.Subsets
Meaning of subsets, notation, examples, proper subsets, and simple ways to check if one set is contained in another.
12.Proper Subset
Meaning of a proper subset, key conditions, examples, and how it differs from a regular subset.
13.Power Set
Meaning of a power set, how to list all subsets of a set, examples, and the formula for the number of subsets.
14.Universal Set
Meaning of a universal set, notation, examples, and how it helps define other sets under discussion.
15.Intervals as Sets
Meaning of intervals as sets, open and closed intervals, notation, and simple examples showing ranges of real numbers.
16.Venn Diagrams – Basics
Basics of Venn diagrams, meaning, purpose, notation, and simple examples showing how sets are represented visually.
17.Venn Diagrams with Two Sets
Understanding two-set Venn diagrams, regions, intersections, unions, complements, and clear examples.
18.Venn Diagrams with Three Sets
Explanation of three-set Venn diagrams, regions, intersections, unions, complements, and clear examples.
19.Overview of Set Operations
Overview of basic set operations such as union, intersection, difference, complement, and their meanings with simple examples.
20.Union of Sets
Meaning of the union of sets, notation, examples, and how union combines elements from two or more sets.
21.Intersection of Sets
Meaning of intersection of sets, notation, examples, and how it identifies common elements between sets.
22.Difference of Sets
Meaning of the difference of sets, notation, examples, and how to find elements that belong to one set but not the other.
23.Symmetric Difference of Sets
Meaning of the symmetric difference of sets, notation, examples, and how it finds elements that are in either set but not in both.
24.Complement of a Set
Meaning of the complement of a set, notation, examples, and how it represents elements outside a set within the universal set.
25.Algebra of Sets
Basic laws of set algebra including commutative, associative, distributive, identity, and De Morgan’s laws with simple explanations and examples.
26.Commutative Laws of Sets
Explanation of commutative laws for union and intersection with simple meanings and examples.
27.Associative Laws of Sets
Associative laws for union and intersection with clear meaning, formulas, and simple examples.
28.Distributive Laws of Sets
Distributive laws for union and intersection with clear formulas, explanations, and simple examples.
29.De Morgan’s Laws
Explanation of De Morgan’s laws for sets with simple meanings, symbols, and examples applying complements to unions and intersections.
30.Dual of Set Statements
Meaning of duality in set statements, how union and intersection interchange, and simple examples showing dual pairs.
31.Principle of Inclusion and Exclusion
Explanation of the principle of inclusion and exclusion for counting elements in unions of sets with clear formulas and examples.
32.Standard Set Identities
List of standard set identities with simple meanings, formulas, and key relationships used in simplifying set expressions.
33.Ordered Pairs
Meaning of ordered pairs, how order matters, notation, and simple examples showing pairs of related elements.
34.Cartesian Product
Meaning of the Cartesian product, how it forms ordered pairs from two sets, with notation and simple examples.
35.Applications of Sets
Common applications of sets in daily life, mathematics, computer science, data handling, and problem-solving.
36.Word Problems Based on Sets
Simple word problems involving sets, unions, intersections, Venn diagrams, and counting overlaps with step-by-step reasoning.