A direct statement on the course's purpose. It establishes the critical role of set theory as the foundational language for all quantitative and logical disciplines.

Provides a precise definition of a mathematical set. The lesson covers the two essential methods for describing a set's elements: the roster form and set-builder notation.

The membership notation of a set helps us express whether a particular object belongs to a given set or not. Using the symbols ∈ (is an element of) and ∉ (is not an element of), we can clearly show the relationship between elements and sets. By the end of this lesson, students will be able to interpret and use membership notation correctly to identify whether or not an element belongs to a set.

A finite set contains a countable number of elements, whereas an infinite set does not. This lesson defines both types of sets, illustrates them with examples, and explains the significance of distinguishing between the two. It also introduces the concept of cardinality and discusses how it applies to both finite and infinite sets.

This lesson introduces three fundamental types of sets. The singleton set contains exactly one element. The empty set (or null set) contains no elements at all. The universal set includes all elements under consideration in a given context or problem. Understanding these special sets is essential, as they form the foundation for more advanced ideas in set theory.

This lesson explains the concept of a subset, where all elements of one set are contained within another. The distinction between a subset and a proper subset is clarified. Equality of sets are explained in terms of subsets.

Here, we prove that an empty set is a subset of every set.

In this lesson, we define the sets of natural numbers, integers, rational numbers, irrational numbers and real numbers along with their relationship using set inclusion. Standard notations for describing these sets are also mentioned.

Introduces the power set of a given set A as the set of all possible subsets of A. The notation and its relationship to cardinality are covered.

Defines the union of two or more sets as the set containing all elements from the original sets. It covers the notation and fundamental properties of the union operation.

Defines the intersection of sets as the set containing only the elements common to all original sets. Notation and properties are detailed.

This lesson defines the finite union. It demonstrates the notation and method for combining a finite number of sets into a single set, with duplicate elements removed.

This lesson defines the finite intersection and disjoint sets. It covers the notation and method for identifying all elements common to a finite collection of sets.

Covers the definition of the complement of a set relative to a universal set. It explains how to determine the elements not present in a given set.

This lesson defines the set difference operation. It covers the notation and method for creating a set containing only the elements of one set that are not in another.

This lesson defines the symmetric difference of two sets. It covers the notation and method for identifying the set of elements present in exactly one of the two sets.

This lesson defines the Venn diagram as the standard tool for visually representing sets and their relationships. We will establish the fundamental conventions required to translate abstract set notation into a clear graphical format for analysis.

This lesson covers De Morgan's Laws, using Venn diagrams for visual proof. Master this graphical method to confirm abstract set identities and verify the results of complement and intersection/union operations.

This lesson details the standard construction for a three-set Venn diagram. We will identify and define five unique regions created by their intersection. Mastery of this model is required for solving complex cardinality problems.

A concise review of the key definitions, notations, and operations covered in the course. This lesson ensures all foundational material has been consolidated.