Set Theory

This topic covers concepts, such as Sets, Definition of a Set, Set Theory Symbols, Element of a Set, Cardinality of a Set, Representation of Sets, Representation of Sets: Roster Method, Representation of Sets: Set-builder Method, Representation of Sets: Venn Diagram & Sets and Relations etc.

This topic covers concepts, such as Types of Sets, Null Set or Empty Set, Singleton Set, Finite Set, Infinite Set, Universal Set, Relation between Two Sets, Equal Sets, Equivalent Sets & Disjoint Sets etc.

This topic covers concepts, such as Subset of a Set, Proper Subsets of a Set, Number of Subsets of a Set, Power Set of a Set, Superset of a Set, Subsets of Set of Real Numbers, Intervals as Subsets of R, Open and Close Intervals, Semi-Open Interval & Length of an Interval etc.

This topic covers concepts, such as Algebraic Operations on Sets, Union of Two Sets, Number of Elements in Union of Two Sets, Union of Two Disjoint Sets, Number of Elements in Union of Two Disjoint Sets, Venn Diagram Presentation of Union of Two Sets, Union of Three Sets, Number of Elements in Union of Three Sets, Number of Elements in Union of Three Disjoint Sets, Venn Diagram Presentation for Union of Three Sets, Intersection of Two Sets, Number of Elements in Intersection of Two Sets, Venn Diagram Presentation of Intersection of Sets, Difference of Two Sets, Venn Diagram Presentation of Difference of Sets, Number of Elements in Difference of Two Sets, Symmetric Difference of Sets, Venn Diagram Presentation of Symmetric Difference of Sets, Number of Elements in Symmetric Difference of Two Sets, Complement of a Set, Venn Diagram Presentation of Complement of a Set, Number of Elements in Complement of a Set, Properties of Complement Sets, Complements Laws, De Morgan's Laws for Complement Sets, Law of Double Complementation, Complement Laws for Empty and Universal Sets, Important Results on Number of Element in Sets Union and Intersection, Properties of Algebraic Operations on Sets, Properties of the Operation of Union, Closure Property of Union of Sets, Idempotent Property of Sets' Union, Commutative Property of Sets' Union, Associative Property of Sets' Union, Existence of Identity for Sets' Union, Non-existence of Inverse for Sets' Union, Law of U for Union of Sets, Properties of the Operation of Intersection, Idempotent Property of Sets' Intersection, Commutative Property of Sets' Intersection, Associative Property of Sets' Intersection, Existence of Identity for Sets' Intersection, Non-existence of Inverse for Sets' Intersection, Law of φ and U for Intersection of Sets, Closure Property of Intersection of Sets, Distributive Property of Sets' Intersection over Union & Practical Problems on Union and Intersection of Two Sets etc.