Complement (set theory)

What is a Set Complement?

What is the complement of a set? Sets in mathematics are very cool, and one of my favorite thins in set theory is the complement and the universal set. In this video we will define complement in set theory, and in order to do so you will also need to know the meaning of universal set. I go

From playlist Set Theory

Set Theory Proof with Complements

Set Theory Proof with Complements

From playlist Set Theory

Double Complement of a Set | Set Theory

What is the complement of the complement of a set? In today's set theory lesson we'll discuss double complements with respect to "absolute complements - being complements taken with respect to a universal set as opposed to relative complements. When we consider a universal set, every oth

From playlist Set Theory

Complement of the Union of Complements | Set Theory

What is the complement of the union of complement sets? We'll go over just that, using DeMorgan's laws for sets in today's set theory lesson! Here are some relevant lessons you may be interested in after or before watching this one... What is a Set Complement? https://www.youtube.com/wat

From playlist Set Theory

Set Complement Example Problems | Set Theory

We go over several practice exercises involving the relative complement of sets and the absolute complement of sets. We also go over a few general examples of set complement involving arbitrary sets: a universal set U, a subset S, and the empty set. What is a Set Complement: https://www.

From playlist Set Theory

Proof: A is a Subset of B' iff A intersect B is Empty | Set Theory, Set Complements

A is a subset of the complement of B if and only if A intersect B is the empty set! We prove this simple set theory result in today's set theory video lesson! Remember that the complement of a set A is the set of all elements not in A, typically this is taken relative to some "universal s

From playlist Set Theory

Introduction to sets || Set theory Overview - Part 2

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty

From playlist Set Theory

Proof: A'-B' = B-A (Double Inclusion) | Set Theory

We prove A'-B'=B-A. That is, the complement of A minus the complement of B equals B minus A. We prove this using double inclusion, meaning we prove both sets are subsets of each other, which by definition establishes set equality. This will require basic applications of set theory definiti

From playlist Set Theory

Proof: A is a Subset of B' iff B is a subset of A' | Set Theory, Set Complements

Let A and B be subsets of a third set S. Then A is a subset of the complement of B (written B') if and only if B is a subset of A'. In this context, by B' we mean all elements of S that are not in B, and similarly for A'. We prove this simple set theory result in today's lesson! Note the

From playlist Set Theory

Proof: DeMorgan's Laws for Set Complement | Set Theory

DeMorgan's laws for sets tell us how set complement works over set union, and how set complement works over intersection. We'll be proving the two parts of De Morgan's laws in today's set theory video lesson! This is a simple proof using our definitions of set union, set intersection, set

From playlist Set Theory

Proof: A is a Subset of B iff B' is Subset of A' | Set Theory, Subsets, Set Complement

Let A and B be two subsets of a third set S. Then A is a subset of B if any only if B’ is a subset of A’. We write B’ to indicate the complement of B, which in this context is the set of elements in S but not in B. We would call S the universal set. We will prove this biconditional resul

From playlist Set Theory

Intro to Set Theory

This video covers the basic concepts of Set Theory: what is a set, union and intersection, subsets, the integers, rational and real numbers. Venn diagrams are used to explain De Morgan's Laws and I provide the beginnings of a proof.

From playlist Foundational Math

How to do a PROOF in SET THEORY - Discrete Mathematics

We learn how to do formal proofs in set theory using intersections, unions, complements, and differences. 0:00 - [Intro] 0:49 - [Language of Set Theory] 3:31 - [Proof #1] 6:15 - [Proof #2] 11:12 - [Proof #3] 14:25 - [Proof #4] #SetTheory #Proofs #DiscreteMath Support me on Patreon: http

From playlist Discrete Math 1

Proof: A Graph or its Complement is not Bipartite | Graph Theory, Bipartite Graphs

If G is a graph with at least 5 vertices, at most one of G or G complement is bipartite. We will prove this graph theory result directly using the well know bipartite graph theorem relating to odd cycles. The only way the statement is false is if there exists a graph G of order 5 or more

From playlist Graph Theory

(PP 1.2) Measure theory: Sigma-algebras

Definition of a sigma-algebra. A playlist of the Probability Primer series is available here: http://www.youtube.com/view_play_list?p=17567A1A3F5DB5E4 You can skip the measure theory (Section 1) if you're not interested in the rigorous underpinnings. If you choose to do this, you

From playlist Probability Theory

What is Set Subtraction?

What is set subtraction? In this video we go over that, the set minus set operation, and an example of subtraction in set theory. This is a handy concept to grasp to understand the complement of a set and universal sets, which I also have videos on. Links below. I hope you find this vide

From playlist Set Theory