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Chapter 1: Sets (108 videos)

1.1: Revision
1. Set Definition
 
1.2: Some Important Sets of Numbers
1. Definition & Notation of Some Important Sets
2. Set Notation & its Characteristics
3. Presentation of a Set
4. Problem 1: Presentation of a Set
5. Set Builder Notation
6. Problem 1: Set Builder Notation
7. Empty Set & Singleton Set
8. Problem 1: Empty Set & Singleton Set
9. Finite & Infinite Set
10. Problem 1: Finite & Infinite Set
11. Equal & Equivalent Sets
12. Problem 1: Equal & Equivalent Sets
13. Subset Definition
14. Problem 1: Subset Definition
15. Proper Subset & Improper Subset
16. Problem 1: Proper Subset & Improper Subset
17. Properties of Subset
18. Problem 1: Properties of Subset
19. Power Set
20. Problem 1: Power Set
 
1.3: Operations on Two Sets
1. Union of Two Sets
2. Problem 1: Union of Two Sets
3. Intersection of Set
4. Problem 1: Intersection of Set
5. Difference of Sets
6. Problem 1: Difference of Sets
7. Symmetric Difference of two sets
8. Problem 1: Symmetric Difference of two sets
9. Universal Set
10. Complement of a Set
11. Problem 1: Complement of a Set
 
1.4: Operations of Union and Intersection on Three Sets
1. Operations of Union and Intesection on three sets
 
1.5: Properties of Union and Intersection for Two or Three Sets
1. Commutative Property of Union
2. Associative Property of Union of Sets
3. Problem 1: Associative Property of Union of Sets
4. Associative Property of Intersection of Sets
5. Problem 1: Associative Property of Intersection of Sets
6. Distributive Property of Union Over Intersection
7. Problem 1: Distributive Property of Union Over Intersection
8. Distributive property of Intersection over Union
9. Problem 1: Distributive property of Intersection over Union
 
1.6: De Morgans Laws
1. Demorgan Law 1
2. Problem 1: Demorgan Law 1
3. Demorgan Law 2
4. Problem 1: Demorgan Law 2
 
1.7: Venn Diagrams
1. Introduction to Venn Diagrams
2. Problem 1: Introduction to Venn Diagrams
3. Commutative Law of Union of Sets
4. Problem 1: Commutative Law of Union of Sets
5. Commutative Law of Intersection of Sets
6. Problem 1: Commutative Law of Intersection of Sets
7. Intersection Associativity for Overlapping Sets
8. Problem 1: Intersection Associativity for Overlapping Sets
9. Intersection Associativity for Disjoint Sets
10. Problem 1: Intersection Associativity for Disjoint Sets
11. Intersection Associativity for Sets
12. Problem 1: Intersection Associativity for Sets
13. More on Intersection Associativity for Sets
14. Problem 1: More on Intersection Associativity for Sets
15. Union Associativity for Overlapping Sets
16. Problem 1: Union Associativity for Overlapping Sets
17. Union Associativity for Disjoint Sets
18. Problem 1: Union Associativity for Disjoint Sets
19. Union Associativity for Sets
20. Problem 1: Union Associativity for Sets
21. More on Union Associativity for Set
22. Problem 1: More on Union Associativity for Set
23. Distributivity of Union Over Intersection of Sets
24. Problem 1: Distributivity of Union Over Intersection of Sets
25. Distributivity of Intersection Over Union of Sets
26. Problem 1: Distributivity of Intersection Over Union of Sets
27. Difference of Sets for Overlapping Sets
28. Problem 1: Difference of Sets for Overlapping Sets
29. Difference of Sets for Disjoint Sets
30. Problem 1: Difference of Sets for Disjoint Sets
31. Difference of Sets for a Set & its Subset
32. Problem 1: Difference of Sets for a Set & its Subset
33. Complement of Union for Overlapping Sets
34. Problem 1: Complement of Union for Overlapping Sets
35. Complement of Intersection for Overlapping Sets
36. Problem 1: Complement of Intersection for Overlapping Sets
37. Complement of Intersection for Disjoint Sets
38. Problem 1: Complement of Intersection for Disjoint Sets
39. Complement of Union for Disjoint Sets
40. Problem 1: Complement of Union for Disjoint Sets
41. Complement of Union for Set & its Subset
42. Problem 1: Complement of Union for Set & its Subset
43. Complement of Intersection for Set & its Subset
44. Problem 1: Complement of Intersection for Set & its Subset
 
1.8: Ordered Pairs
1. Introduction to Ordered Pairs
 
1.9: Cartesian Product of Sets
1. Cartesian Product of Sets
2. Problem 1: Cartesian Product of Sets
 
1.10: Binary Relation
1. Introduction to Binary Relation
2. Problem 1: Introduction to Binary Relation
3. Domain & Range of Binary Relation
4. Problem 1: Domain & Range of Binary Relation
 
1.11: Functions
1. Introduction to Function
2. Problem 1: Introduction to Function
3. Onto Function
4. Problem 1: Onto Function
5. One to One Function
6. Problem 1: One to One Function
7. Bijective Function
8. Problem 1: Bijective Function
 
1.12: Cartesian Coordinate System for Plane
1. Cartesian Coordinate System & Cartesian Plane
2. Problem 1: Cartesian Coordinate System & Cartesian Plane
 
1.13: Graphical Representation of Cartesian Product
1. Introduction to Graphs
 

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