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Chapter 2: Sets, Functions and Groups (267 videos)

2.1: Introduction
1. Set Definition
2. Problem-Set Definition
3. Set Notation & its Characteristics
4. Problem-Set Notation & its Characteristics
5. Presentation of a Set
6. Problem-Presentation of a Set
7. Problem 1: Presentation of a Set
8. Empty Set & Singleton Set
9. Problem 1: Empty Set & Singleton Set
10. Problem-Empty Set & Singleton Set
11. Finite & Infinite Set
12. Problem 1: Finite & Infinite Set
13. Problem-Finite & Infinite Set
14. Subset Definition
15. Problem 1: Subset Definition
16. Problem-Subset Definition
17. Proper Subset & Improper Subset
18. Problem 1: Proper Subset & Improper Subset
19. Properties of Subset
20. Problem 1: Properties of Subset
21. Power Set
22. Problem 1: Power Set
23. Equal & Equivalent Sets
24. Problem 1: Equal & Equivalent Sets
25. Universal Set
26. Definition of One to One Correspondence
27. Definition & Notation of Some Important Sets
28. Problem 1: Set Builder Notation
29. Order of a Set
30. Problem-Order of a Set
31. Interval Notation of a Set
 
2.2: Operations on Sets
1. Disjoint Set
2. Overlapping Sets
3. Union of Two Sets
4. Problem 1: Union of Two Sets
5. Exhaustive Sets and Cells
6. Intersection of Set
7. Problem 1: Intersection of Set
8. Difference of Sets
9. Problem 1: Difference of Sets
10. Symmetric Difference of two sets
11. Problem 1: Symmetric Difference of two sets
12. Complement of a Set
13. Problem 1: Complement of a Set
 
2.3: Venn Diagrams
1. Introduction to Venn Diagrams
2. Problem 1: Introduction to Venn Diagrams
3. Difference of Sets for Overlapping Sets
4. Problem 1: Difference of Sets for Overlapping Sets
5. Difference of Sets for Disjoint Sets
6. Problem 1: Difference of Sets for Disjoint Sets
7. Difference of Sets for a Set & its Subset
8. Problem 1: Difference of Sets for a Set & its Subset
9. Complement of Union for Overlapping Sets
10. Problem 1: Complement of Union for Overlapping Sets
11. Complement of Intersection for Overlapping Sets
12. Problem 1: Complement of Intersection for Overlapping Sets
13. Complement of Intersection for Disjoint Sets
14. Problem 1: Complement of Intersection for Disjoint Sets
15. Complement of Union for Disjoint Sets
16. Problem 1: Complement of Union for Disjoint Sets
17. Complement of Union for Set & its Subset
18. Problem 1: Complement of Union for Set & its Subset
19. Complement of Intersection for Set & its Subset
20. Problem 1: Complement of Intersection for Set & its Subset
21. Demorgans Law for Overlapping Sets
22. Problem 1: Demorgans Law for Overlapping Sets
23. Identity Laws
24. Problem-Identity Laws
25. Laws of Complement
26. Problem-Laws of Complement
27. Some Important Laws
28. Problem-Some Important Laws
29. Demorgans Law for Disjoint Sets
30. Problem 1: Demorgans Law for Disjoint Sets
31. Demorgans Law for Set & its Subset
32. Problem 1: Demorgans Law for Set & its Subset
 
2.4: Operations on Three Sets
1. Associative Property of Union of Sets
2. Problem 1: Associative Property of Union of Sets
3. Associative Property of Intersection of Sets
4. Problem 1: Associative Property of Intersection of Sets
5. Distributive Property of Union Over Intersection
6. Problem 1: Distributive Property of Union Over Intersection
7. Double Complementation Law
8. Problem-Double Complementation Law
9. Operations of Union and Intesection on three sets
10. Commutative Property of Union
11. Commutativity of Intersection
12. Distributive property of Intersection over Union
13. Problem 1: Distributive property of Intersection over Union
14. Distributive Property of Cartesian Product Over Union
15. Problem-Distributive Property of Cartesian Product Over Union
16. Distributive Property of Cartesian Product Over Intersection
17. Problem-Distributive Property of Cartesian Product Over Intersection
18. Distributive Property of Cartesian Product Over Difference
19. Problem-Distributive Property of Cartesian Product Over Difference
20. Identity With Respect to Intersection
21. Problem-Identity With Respect to Intersection
 
2.5: Properties of Union and Intrersection
1. Associative Property of Union of Sets
2. Problem 1: Associative Property of Union of Sets
3. Associative Property of Intersection of Sets
4. Problem 1: Associative Property of Intersection of Sets
5. Distributive Property of Union Over Intersection
6. Problem 1: Distributive Property of Union Over Intersection
7. Demorgan Law 1
8. Problem 1: Demorgan Law 1
9. Demorgan Law 2
10. Problem 1: Demorgan Law 2
11. Introduction to Venn Diagrams
12. Problem 1: Introduction to Venn Diagrams
13. Commutative Law of Union of Sets
14. Problem 1: Commutative Law of Union of Sets
15. Commutative Law of Intersection of Sets
16. Problem 1: Commutative Law of Intersection of Sets
17. Intersection Associativity for Overlapping Sets
18. Problem 1: Intersection Associativity for Overlapping Sets
19. Intersection Associativity for Disjoint Sets
20. Problem 1: Intersection Associativity for Disjoint Sets
21. Intersection Associativity for Sets
22. More on Intersection Associativity for Sets
23. Problem 1: Intersection Associativity for Sets
24. Problem 1: More on Intersection Associativity for Sets
25. Union Associativity for Overlapping Sets
26. Problem 1: Union Associativity for Overlapping Sets
27. Union Associativity for Disjoint Sets
28. Problem 1: Union Associativity for Disjoint Sets
29. Union Associativity for Sets
30. Problem 1: Union Associativity for Sets
31. More on Union Associativity for Set
32. Problem 1: More on Union Associativity for Set
33. Distributivity of Union Over Intersection of Sets
34. Problem 1: Distributivity of Union Over Intersection of Sets
35. Distributivity of Intersection Over Union of Sets
36. Problem 1: Distributivity of Intersection Over Union of Sets
37. Difference of Sets for Overlapping Sets
38. Problem 1: Difference of Sets for Overlapping Sets
39. Difference of Sets for Disjoint Sets
40. Problem 1: Difference of Sets for Disjoint Sets
41. Difference of Sets for a Set & its Subset
42. Problem 1: Difference of Sets for a Set & its Subset
43. Complement of Union for Overlapping Sets
44. Problem 1: Complement of Union for Overlapping Sets
45. Complement of Intersection for Overlapping Sets
46. Problem 1: Complement of Intersection for Overlapping Sets
47. Complement of Intersection for Disjoint Sets
48. Problem 1: Complement of Intersection for Disjoint Sets
49. Complement of Union for Disjoint Sets
50. Problem 1: Complement of Union for Disjoint Sets
51. Complement of Union for Set & its Subset
52. Problem 1: Complement of Union for Set & its Subset
53. Complement of Intersection for Set & its Subset
54. Problem 1: Complement of Intersection for Set & its Subset
55. Demorgans Law for Overlapping Sets
56. Problem 1: Demorgans Law for Overlapping Sets
57. Demorgans Law for Disjoint Sets
58. Problem 1: Demorgans Law for Disjoint Sets
59. Demorgans Law for Set & its Subset
60. Problem 1: Demorgans Law for Set & its Subset
 
2.6: Inductive and Deductive Logic
1. Concept of Induction and Deduction
2. Problem-Concept of Induction and Deduction
3. Aristotelian and Non Aristotelian Logics
4. Problem-Aristotelian and Non Aristotelian Logics
5. Symbolic Logics
6. Problem-Symbolic Logics
 
2.7: Implication or Conditional
1. Introduction to Implication or Conditional
2. Problem-Introduction to Implication or Conditional
3. Concept of Bi-Conditional
4. Problem-Concept of Bi-Conditional
5. Conditionals Related with a Given Conditional
6. Problem-Conditionals Related with a Given Conditional
7. Introducing Tautologies
8. Problem-Introducing Tautologies
9. Introducing Quantifiers
 
2.8: Truth Sets, A Link Between Sets Theory and Logic
1. A link Between Set Theory and Logic
2. More on A link Between Set Theory and Logic
3. Further on A link Between Set Theory and Logic
4. Problem-A link Between Set Theory and Logic
 
2.9: Relations
1. Introduction to Binary Relation
2. Problem-Introduction to Binary Relation
3. Problem 1: Introduction to Binary Relation
4. Domain & Range of Binary Relation
5. Problem 1: Domain & Range of Binary Relation
6. Problem-Domain & Range of Binary Relation
 
2.10: Functions
1. Introduction to Function
2. More on Introduction to Functions
3. Problem 1: Introduction to Function
4. Problem-Introduction to Function
5. Problem3-Introduction to Function
6. Problem4-Introduction to Function
7. Implied Domain
8. Finding Domain and Range of Functions
9. Types of Relations
10. Operations on Functions
11. Into Function
12. Problem 1: Into Function
13. Problem-Into Function
14. Onto Function
15. Problem 1: Onto Function
16. Problem-Onto Function
17. One to One Function
18. Problem 1: One to One Function
19. Problem-One to One Correspondence
20. Bijective Function
21. Problem 1: Bijective Function
22. Problem-Bijective Function
23. Injective Function
24. Problem 1: Injective Function
25. Problem-Injective Function
26. One-One Function
27. Problem-One-One Function
28. Set Builder Notation for a Function
29. Problem-Set Builder Notation for a Function
30. Formulization of Functions
31. Algebraic Functions
32. Linear and Quadratic Functions
33. Problem-Linear and Quadratic Functions
34. Sketching Graphs of Quadratic Functions
35. Problem-Sketching Graphs of Quadratic Functions
 
2.11: Inverse of a Function
1. Inverse of a Function
2. More on Inverse of a Functions
3. Problem1-Inverse of a Function
4. Problem-Inverse of a Function
5. Domain & Range of Inverse Function
6. Square Root and Absolute Value Functions
7. Problem-Square Root and Absolute Value Functions
8. Constant, Identity and Rational Functions
9. Problem-Constant, Identity and Rational Functions
10. Even and Odd Functions
11. Problem-Even and Odd Functions
12. The Modulus of a Function
 
2.12: Binary Operations
1. Introduction to Binary Operations
2. Problem-Introduction to Binary Operations
3. Multiplication Table
4. Problem-Multiplication Table
5. Operations on Residue Classes Modulo n
6. Problem-Operations on Residue Classes Modulo n
7. Properties of Binary Operations
8. Problem-Properties of Binary Operations
9. Theorems on Binary Operation
10. More on Theorems on Binary Operation
11. Problem-Theorems on Binary Operation
 
2.13: Groups
1. Introduction to Semi-Group
2. Problem-Introduction to Semi-Group
3. Introduction to Groups
4. Problem-Introduction to Groups
5. Introduction to Abelian and Non-Abelian Group
6. Problem-Introduction to Abelian and Non-Abelian Group
7. Finite and Infinite Group
8. Problem1-Finite and Infinite Group
9. Problem2-Finite and Infinite Group
 
2.14: Solution of Linear Equations
1. Solution of Simple Linear Equations in one Variables
2. Problem 1: Solution of Simple Linear Equations in one Variables
3. Problem-Solution of Linear Equations
 
2.15: Reversal Law of Inverse
1. Introduction to Reversal Laws of Inverses
2. Problem-Introduction to Reversal Laws of Inverses
3. Theorems on Groups
4. More on Theorems on Groups
5. Problem-Theorems on Groups
6. Problem-Theorems on Abelian Groups
7. Composition of a Functions
8. Problem-Composition of Functions
9. Logical Proofs of the Operations on Sets
10. More on Logical Proofs of the Operations on Sets
11. The Set of Rational Numbers is an Abelian Group
12. The Set of Non-Zero Real Numbers is an Abelian Group
13. The Set of Complex Numbers is an Abelian Group
14. Algebraic Method to find the Inverse Function
15. Problem-Algebraic Method to find the Inverse Function
 

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