Math: Sets & Set Theory

We often deal with groups or collection of objects in real life, such a set of books, a group of students, a team of basketball players, a list of states in a country, a collection of baseball cards, etc.

Sets may be thought of as a mathematical way to represent collections or groups of objects. The concept of sets is an essential foundation for various other topics in mathematics.

This series of lessons cover the essential concepts of math set theory - the basic ways of describing sets, use of set notation, finite sets, infinite sets, empty sets, subsets, universal sets, complement of a set, basic set operations including intersection and union of sets, using Venn diagrams and simple applications of sets.

Sets
Introduction to sets	Set Operations	Lessons about Sets
Lectures about sets	Sets Worksheets	Math Worksheets

Introduction To Sets

Describing Sets
Set Notation
Finite & Infinite Sets
Empty Set Or Null Set
Set Equality

Venn Diagrams
Subsets
Universal Set
Complement Of A Set

Set Operations

Intersection of Two Sets
Intersection of Three Sets
Complement of an Intersection
Union Of Sets
Combined Operations Of Sets

Drawing Venn Diagrams
De Morgan’s Theorem
Shading Venn Diagrams

Lessons About Sets

Set Notation
Roster method, set-builder notation, Venn diagrams

Universal Sets & Subsets
Sets, universal sets, subsets, equal sets, disjoint sets

Set Operations
union, intersection, complement

Venn Diagrams I
Venn Diagrams to represent Union, Intersection and Complement

Venn Diagrams II
Venn diagrams with 3 sets and 2 sets

Venn Diagram Word Problems
How to solve word problems using Venn Diagrams?

A Series Of Lectures On Sets

These are at an advanced level, suitable for undergraduate studies.

Definition of a Set
Russell’s paradox, logical implications, converse, contrapositive, truth tables

Operations on Sets
The concept of negation, union, intersection, complement, difference, symmetric difference

De Morgan’s law & Logic
What is De Morgan’s Law and proof of De Morgan’s Law

Power Sets
The Power Set And Investigating How Many Elements The Power Set Has.

Sets Worksheets

Set Notations
A quiz to test your knowledge of set notations: intersection, union, subset, etc.

Elements in a Set
Determine whether an element is a member of a given set and the number of members in a given set.

Types of Sets
Determine whether a given set is an infinite set, finite set or empty set.

Subsets
Distinguish between subsets and proper subsets. Find the number of subsets in a given set.

Complement of a Set
Universal set, complement of a set, and subsets.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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