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Sets, Functions and Groups
Federal Board > Class 11 > Math (
Total Videos: 1130
)
All Chapters
Chapter 1: Numbers System
Chapter 2: Sets, Functions and Groups
Chapter 3: Matrices and Determinants
Chapter 4: Quadratic Equations
Chapter 5: Partial Fractions
Chapter 6: Sequences and Series
Chapter 7: Permutation, Combination and Probability
Chapter 8: Mathematical Inductions and Binomial Theorems
Chapter 9: Fundamentals of Trigonometry
Chapter 10: Trigonometric Identities Sum and Difference of Angles
Chapter 11: Trigonometric Functions and Their Graphs
Chapter 12: Application of Trigonometry
Chapter 13: Inverse Trigonometric Functions
Chapter 14: Solutions of Trigonometric Equations
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Chapter 2: Sets, Functions and Groups (
265 videos
)
  (
Practice Test
)
2.1: Introduction(
Practice Test
)
Set Definition
Problem-Set Definition
Set Notation & its Characteristics
Problem-Set Notation & its Characteristics
Problem-Presentation of a Set
Empty set and Singleton Set
Problem 1: Empty Set & Singleton Set
Problem-Empty Set & Singleton Set
Finite & Infinite Set
Problem 1: Finite & Infinite Set
Problem-Finite & Infinite Set
Subset Definition
Problem 1: Subset Definition
Problem-Subset Definition
Proper Subset & Improper Subset
Problem 1: Proper Subset & Improper Subset
Properties of Subset
Problem 1: Properties of Subset
Power Set
Problem 1: Power Set
Equal & Equivalent Sets
Problem 1: Equal & Equivalent Sets
Universal Set
Definition of One to One Correspondence
Definition & Notation of Some Important Sets
Presentation of a Set
Problem 1: Set Builder Notation
Order of a Set
Problem-Order of a Set
Interval Notation of a Set
2.2: Operations on Sets(
Practice Test
)
Disjoint Set
Overlapping Sets
Union of Two Sets
Problem 1: Union of Two Sets
Exhaustive Sets and Cells
Intersection of Set
Problem 1: Intersection of Set
Difference of Sets
Symmetric Difference of two sets
Problem 1: Symmetric Difference of two sets
Complement of a Set
Problem 1: Complement of a Set
2.3: Venn Diagrams(
Practice Test
)
Introduction to Venn Diagrams
Problem 1: Introduction to Venn Diagrams
Difference of Sets for Overlapping Sets
Problem 1: Difference of Sets for Overlapping Sets
Difference of Sets for Disjoint Sets
Problem 1: Difference of Sets for Disjoint Sets
Difference of Sets for a Set & its Subset
Problem 1: Difference of Sets for a Set & its Subset
Complement of Union for Overlapping Sets
Problem 1: Complement of Union for Overlapping Sets
Complement of Intersection for Overlapping Sets
Problem 1: Complement of Intersection for Overlapping Sets
Complement of Intersection for Disjoint Sets
Problem 1: Complement of Intersection for Disjoint Sets
Complement of Union for Disjoint Sets
Problem 1: Complement of Union for Disjoint Sets
Complement of Union for Set & its Subset
Problem 1: Complement of Union for Set & its Subset
Complement of Intersection for Set & its Subset
Problem 1: Complement of Intersection for Set & its Subset
Demorgans Law for Overlapping Sets
Problem 1: Demorgans Law for Overlapping Sets
Identity Laws
Problem-Identity Laws
Laws of Complement
Problem-Laws of Complement
Some Important Laws
Problem-Some Important Laws
Demorgans Law for Disjoint Sets
Problem 1: Demorgans Law for Disjoint Sets
Demorgans Law for Set & its Subset
Problem 1: Demorgans Law for Set & its Subset
2.4: Operations on Three Sets(
Practice Test
)
Associative Property of Union of Sets
Problem 1: Associative Property of Union of Sets
Associative Property of Intersection of Sets
Problem 1: Associative Property of Intersection of Sets
Distributive Property of Union Over Intersection
Problem 1: Distributive Property of Union Over Intersection
Double Complementation Law
Problem-Double Complementation Law
Operations of Union and Intesection on three sets
Commutative Property of Union
Commutativity of Intersection
Distributive property of Intersection over Union
Problem 1: Distributive property of Intersection over Union
Distributive Property of Cartesian Product Over Union
Problem-Distributive Property of Cartesian Product Over Union
Distributive Property of Cartesian Product Over Intersection
Problem-Distributive Property of Cartesian Product Over Intersection
Distributive Property of Cartesian Product Over Difference
Problem-Distributive Property of Cartesian Product Over Difference
Identity With Respect to Intersection
Problem-Identity With Respect to Intersection
2.5: Properties of Union and Intrersection(
Practice Test
)
Associative Property of Union of Sets
Problem 1: Associative Property of Union of Sets
Associative Property of Intersection of Sets
Problem 1: Associative Property of Intersection of Sets
Distributive Property of Union Over Intersection
Problem 1: Distributive Property of Union Over Intersection
Demorgan Law 1
Problem 1: Demorgan Law 1
Demorgan Law 2
Problem 1: Demorgan Law 2
Introduction to Venn Diagrams
Problem 1: Introduction to Venn Diagrams
Commutative Law of Union of Sets
Problem 1: Commutative Law of Union of Sets
Commutative Law of Intersection of Sets
Problem 1: Commutative Law of Intersection of Sets
Intersection Associativity for Overlapping Sets
Problem 1: Intersection Associativity for Overlapping Sets
Intersection Associativity for Disjoint Sets
Problem 1: Intersection Associativity for Disjoint Sets
Intersection Associativity for Sets
More on Intersection Associativity for Sets
Problem 1: Intersection Associativity for Sets
Problem 1: More on Intersection Associativity for Sets
Union Associativity for Overlapping Sets
Problem 1: Union Associativity for Overlapping Sets
Union Associativity for Disjoint Sets
Problem 1: Union Associativity for Disjoint Sets
Union Associativity for Sets
Problem 1: Union Associativity for Sets
More on Union Associativity for Set
Problem 1: More on Union Associativity for Set
Distributivity of Union Over Intersection of Sets
Problem 1: Distributivity of Union Over Intersection of Sets
Distributivity of Intersection Over Union of Sets
Problem 1: Distributivity of Intersection Over Union of Sets
Difference of Sets for Overlapping Sets
Problem 1: Difference of Sets for Overlapping Sets
Difference of Sets for Disjoint Sets
Problem 1: Difference of Sets for Disjoint Sets
Difference of Sets for a Set & its Subset
Problem 1: Difference of Sets for a Set & its Subset
Complement of Union for Overlapping Sets
Problem 1: Complement of Union for Overlapping Sets
Complement of Intersection for Overlapping Sets
Problem 1: Complement of Intersection for Overlapping Sets
Complement of Intersection for Disjoint Sets
Problem 1: Complement of Intersection for Disjoint Sets
Complement of Union for Disjoint Sets
Problem 1: Complement of Union for Disjoint Sets
Complement of Union for Set & its Subset
Problem 1: Complement of Union for Set & its Subset
Complement of Intersection for Set & its Subset
Problem 1: Complement of Intersection for Set & its Subset
Demorgans Law for Overlapping Sets
Problem 1: Demorgans Law for Overlapping Sets
Demorgans Law for Disjoint Sets
Problem 1: Demorgans Law for Disjoint Sets
Demorgans Law for Set & its Subset
Problem 1: Demorgans Law for Set & its Subset
2.6: Inductive and Deductive Logic(
Practice Test
)
Concept of Induction and Deduction
Problem-Concept of Induction and Deduction
Aristotelian and Non Aristotelian Logics
Problem-Aristotelian and Non Aristotelian Logics
Symbolic Logics
Problem-Symbolic Logics
2.7: Implication or Conditional(
Practice Test
)
Introduction to Implication or Conditional
Problem-Introduction to Implication or Conditional
Concept of Bi-Conditional
Problem-Concept of Bi-Conditional
Conditionals Related with a Given Conditional
Problem-Conditionals Related with a Given Conditional
Introducing Tautologies
Problem-Introducing Tautologies
Introducing Quantifiers
2.8: Truth Sets, A Link Between Sets Theory and Logic(
Practice Test
)
A link Between Set Theory and Logic
More on A link Between Set Theory and Logic
Further on A link Between Set Theory and Logic
Problem-A link Between Set Theory and Logic
2.9: Relations(
Practice Test
)
Introduction to Binary Relation
Problem-Introduction to Binary Relation
Problem2-Introduction to Binary Relation
Domain & Range of Binary Relation
Problem 1: Domain & Range of Binary Relation
Problem-Domain & Range of Binary Relation
2.10: Functions(
Practice Test
)
Introduction to Function
More on Introduction to Functions
Problem 1: Introduction to Function
Problem-Introduction to Function
Problem3-Introduction to Function
Problem4-Introduction to Function
Implied Domain
Finding Domain and Range of Functions
Types of Relations
Operations on Functions
Into Function
Problem 1: Into Function
Problem-Into Function
Onto Function
Problem 1: Onto Function
Problem-Onto Function
One to One Function
Problem 1: One to One Function
Problem-One to One Correspondence
Bijective Function
Problem 1: Bijective Function
Problem-Bijective Function
Injective Function
Problem 1: Injective Function
Problem-Injective Function
One-One Function
Problem-One-One Function
Set Builder Notation for a Function
Problem-Set Builder Notation for a Function
Formulization of Functions
Algebraic Functions
Linear and Quadratic Functions
Problem-Linear and Quadratic Functions
Sketching Graphs of Quadratic Functions
Problem-Sketching Graphs of Quadratic Functions
2.11: Inverse of a Function(
Practice Test
)
Inverse of a Function
More on Inverse of a Functions
Problem1-Inverse of a Function
Problem-Inverse of a Function
Domain & Range of Inverse Function
Square Root and Absolute Value Functions
Problem-Square Root and Absolute Value Functions
Constant, Identity and Rational Functions
Problem-Constant, Identity and Rational Functions
Even and Odd Functions
Problem-Even and Odd Functions
The Modulus of a Function
2.12: Binary Operations(
Practice Test
)
Introduction to Binary Operations
Problem-Introduction to Binary Operations
Multiplication Table
Problem-Multiplication Table
Operations on Residue Classes Modulo n
Problem-Operations on Residue Classes Modulo n
Properties of Binary Operations
Problem-Properties of Binary Operations
Theorems on Binary Operation
More on Theorems on Binary Operation
Problem-Theorems on Binary Operation
2.13: Groups(
Practice Test
)
Introduction to Semi-Group
Problem-Introduction to Semi-Group
Introduction to Groups
Problem-Introduction to Groups
Introduction to Abelian and Non-Abelian Group
Problem-Introduction to Abelian and Non-Abelian Group
Finite and Infinite Group
Problem1-Finite and Infinite Group
Problem2-Finite and Infinite Group
2.14: Solution of Linear Equations
Solution of Simple Linear Equations in one Variables
Problem 1: Solution of Simple Linear Equations in one Variables
Problem-Solution of Linear Equations
2.15: Reversal Law of Inverse(
Practice Test
)
Introduction to Reversal Laws of Inverses
Problem-Introduction to Reversal Laws of Inverses
Theorems on Groups
More on Theorems on Groups
Problem-Theorems on Groups
Problem-Theorems on Abelian Groups
Composition of a Functions
Problem-Composition of Functions
Logical Proofs of the Operations on Sets
More on Logical Proofs of the Operations on Sets
The Set of Rational Numbers is an Abelian Group
The Set of Non-Zero Real Numbers is an Abelian Group
The Set of Complex Numbers is an Abelian Group
Algebraic Method to find the Inverse Function
Problem-Algebraic Method to find the Inverse Function
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