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YouTube

Set Theory

Wrath of Math via YouTube

Overview

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Learn fundamental set theory concepts through comprehensive video lessons covering basic definitions, operations, and advanced proofs. Master essential topics including sets, subsets, unions, intersections, complements, and set notation while exploring proper and improper subsets, empty sets, and universal sets. Discover how to work with Venn diagrams to visualize set relationships and operations, calculate cardinalities, and understand power sets and their properties. Explore advanced concepts such as Cartesian products, symmetric differences, disjoint sets, and set partitions. Practice applying the inclusion-exclusion principle for counting problems and learn to construct mathematical proofs involving set relationships and properties. Study important theorems including De Morgan's Laws, distributive properties, and various subset relationships through rigorous mathematical demonstrations. Develop skills in set builder notation, roster method, and tree diagrams for listing subsets. Examine connections between set theory and graph theory through topics like independent vertex sets and resolving sets. Build a solid foundation in mathematical reasoning while working through numerous example problems and exercises that reinforce theoretical concepts with practical applications.

Syllabus

An Introduction to Sets (Set Theory)
Proper Subsets vs Improper Subsets | Set Theory
What is a Union? (Set Theory)
What is an Intersection? (Set Theory)
Union vs Intersection (Set Theory)
What is a Set Complement?
What is Set Subtraction?
What is the Symmetric Difference of 2 Sets?
What are Equal Sets?
How Many Subsets Does any Given Set Have
Why is the Empty Set a Subset of Every Set? | Set Theory, Subsets, Subset Definition
What is a Subset?
Even Numbers in Set Builder Notation
What is the Roster Method? (Roster Form) | Set Theory, Writing Sets, Expressing Sets
Set Union Using Venn Diagrams
Set Intersection Using Venn Diagrams
What is the Cardinality of a Set? | Set Theory, Empty Set
What is a Power Set? | Set Theory, Subsets, Cardinality
What are Disjoint Sets? | Set Theory
What is the Cartesian Product of Sets? | Set Theory
Cartesian Products with Empty Sets | Set Theory, Cartesian Product of Sets, Empty Set
Set Subtraction Using Venn Diagrams | Set Theory
Formula for Cardinality of Power Sets | Set Theory
What is the Power Set of the Empty Set? | Set Theory
How to Find the Median of a Data Set | Statistics
Universal Sets, Absolute Complements, and Venn Diagrams | Set Theory, Sets in Venn Diagrams
What are Elements of Sets? | Set Theory, Cardinality, Set Elements
Universal Set Example Problems | Set Builder Notation, Absolute Complement, Roster Notation
Graph the Set of Solutions to a System of Inequalities | Relations, Algebra, Domain and Range
Caridnality of the Union of Two Sets (Formula Explained) | Set Theory, Cardinality, Set Union
How to Identify the Elements of a Set | Set Theory
Finding the Number of Subsets of a Set (Example Problems)
What are Overlapping Sets? | Set Theory
Basic Set Operations as Venn Diagrams | Set Theory, Set Operations, Set Diagrams
What are Equivalent Sets? | Set Theory, Equipollent Sets, Set Equivalency
Independent Vertex Sets and Independence Numbers | Graph Theory
Counting Problem With Overlapping Sets | Inclusion-Exclusion Principle, Combinatorics
Number of Subsets Containing a Set of Elements | Set Theory, Combinatorics
Listing Subsets Using Tree Diagrams | Set Theory, Subsets, Power Sets
Proof: Subset is a Transitive Relation | Set Theory, Subsets, Transitivity
Proof: If A is a Subset of B then P(A) is a Subset of P(B) | Power Sets, Set Theory
Proof: A is a Subset of B iff A Union B Equals B | Set Theory, Subsets
Proof: A is a Subset of B iff A intersect B Equals A | Set Theory, Subsets
Proof: A is a Subset of B' iff A intersect B is Empty | Set Theory, Set Complements
Proof: A is a Subset of B iff B' is Subset of A' | Set Theory, Subsets, Set Complement
Proof: A is a Subset of B' iff B is a subset of A' | Set Theory, Set Complements
Proof: Idempotent Property of Set Union | Set Theory
Proof: Idempotent Property of Set Intersection | Set Theory
Resolving Sets and Metric Dimension of Graphs | Graph Theory
What are Supersets? | Set Theory, Subsets, Set Relations
Proof on Subsets and Union of Intersections | Set Theory, Set Equality
Proof: A' is a Subset of B iff AUB is Universal Set | Set Theory
Finding Power Set Examples | Set Theory, Subsets and Power Sets
Partitions of a Set | Set Theory
Finding a Set from its Intersection and Relative Complement | Set Theory
Proof: If P(A) is a Subset of P(B) then A is a Subset of B | Set Theory
Proof: Divisors of a Number are a Subset of the Divisors of its Square
Double Complement of a Set | Set Theory
Power Set of the Power Set of the Power Set of the Empty Set | Set Theory
Is Subset an Equivalence Relation? | Set Theory
Finding Cardinalities of Sets | Set Theory
How Many Proper Subsets Does a Set Have? | Set Theory
Why Every Set is a Subset of Itself | Set Theory
Counting Partitions of Sets and Bell Numbers | Combinatorics
Proof: If A is a Subset of B then C-B is a Subset of C-A | Set Theory
Proof: Set Intersection Distributes Over Union | Set Theory
Proof: Set Union Distributes Over Intersection | Set Theory
Complement of the Union of Complements | Set Theory
Set Complement Example Problems | Set Theory
Equal Symmetric Difference Implies Set Equality | Set Theory
A Union B Equals A Intersect B iff A=B | Set Theory
arguing sets joke
Proof: DeMorgan's Laws for Set Complement | Set Theory
Every Set is an Element of its Power Set | Set Theory
Proof: A=B iff P(A)=P(B) (Sets are Equal iff their Power Sets are Equal) | Set Theory
Empty Set vs Set Containing Empty Set | Set Theory
Power Set of Intersection Equals Intersection of Power Sets | Set Theory
Proof: A-B is a Subset of A union B | Set Theory
Proof: Cancellation Law for Cartesian Products | Set Theory
Odd Numbers in Set Builder Notation (Set Builder Form) | Set Theory
Disjoint Sets Examples and Non-Examples | Set Theory
Power Set of the Math Set {m, a, t, h} | Set Theory
Proof: Number of Subsets using Induction | Set Theory
Proof: Cartesian Product with Set Intersection | Set Theory
Cardinality of Sets with Repeated Elements | Set Theory
Proof: A'-B' = B-A (Double Inclusion) | Set Theory
Find All Subsets of a Set (Example Problems) | Set Theory Exercises

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Wrath of Math

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