Set Theory
Set theory is a branch of mathematics that deals with collections of objects. These collections are called sets. A set is simply a group of distinct things, like numbers, letters, or even everyday objects, that are grouped together based on some common property.
- A set is a well-defined collection of distinct objects. These objects are called elements or members of the set. For example:
- A set of fruits:
{apple, banana, orange} - A set of numbers:
{1, 2, 3, 4}
- A set of fruits:
- Notation: Sets are written using curly braces
{}.- Example:
{2, 4, 6}is a set of even numbers.
- Example:
- Membership: If something is in a set, we say it is a member of the set, denoted by
∈. If not, we use∉.- Example: In the set
{1, 2, 3},2 ∈ {1, 2, 3}but5 ∉ {1, 2, 3}.
- Example: In the set
Some examples of sets include:
Key Concepts in Set Theory
- Set in Maths
- Representation of Sets
- Subsets
- Supersets
- Power Set
- Set Theory Symbols
- Set Theory Formulas
- Types of Sets
- Operations on Sets
- Cardinality of Sets
- Venn Diagrams
- De Morgan’s Laws
- Set Notations in LaTeX
Advanced Topics of Set Theory
Practice for Set Theory
Program of Set Theory
Standard Problems Associated with Set Data Structure
- Find Union and Intersection of two unsorted arrays
- Count distinct elements in an array
- Longest Consecutive Subsequence
- Remove duplicates from sorted array
- K’th Smallest/Largest Element in Unsorted Array
FAQs on Set Theory
What is the basic of set theory?
Set Theory is the study of a collection of objects which are called sets and the relation between different sets.
How do you define set?
Set is a well-defined collection of objects. These objects are called the element of sets.
Who Invented set theory?
Set Theory was invented by German Mathematician Georg Cantor.
What is the Algebra of Sets?
Algebra of Sets deals with the following laws:
- Commutative Laws
- Associative Law
- Distributive Law
- Identity Law
- Idempotent Law
These laws are covered in the article under Properties of Sets.
What is a Subset?
A subset is a set that has fewer or equal elements of another set. The other set is called a Superset.
What is De Morgan’s Law?
De Morgan’s Law is a law that deals with the union and intersection of sets with the intersection and union of individual sets respectively. There are two laws under it namely De Morgan’s Law of Union and De Morgan’s Law of Intersection. These are covered under the section of De Morgan’s Law in this article.
