Set Notation


Related Pages
Describing Sets
Venn Diagrams And Subsets
More Lessons On Sets

In these lessons, we will learn the concept of a set, methods for defining sets, set notations, empty set, symbols for ‘is an element of’, subset, intersection and union. These lessons are part of a series of Lessons On Sets.




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Set Notations

The following table gives a summary of the symbols use in sets.

Set Symbols and Notations

A set is a well-defined collection of distinct objects.

The individual objects in a set are called the members or elements of the set.

Some notations for sets are:
{1, 2, 3} = set of integers greater than 0 and less than 4 = {x: x is an integer and 0 < x < 4}

We also have the empty set denoted by {} or Ø, meaning that the set has no elements.

We can have infinite sets for example {1, 2, 3, …}, meaning that the set has an infinite number of elements.

We have a symbol showing membership. We relate a member and a set using the symbol ∈. If an object x is an element of set A, we write x ∈ A. If an object z is not an element of set A, we write z ∉ A.

∈ denotes “is an element of’ or “is a member of” or “belongs to”

∉ denotes “is not an element of” or “is not a member of” or “does not belong to”

Example:
If A = {1, 3, 5} then 1 ∈ A and 2 ∉ A




Video Lessons on Sets

This video introduces the concept of a set and various methods for defining sets.

Set Notation(s): A discussion of set notation: lists, descriptions, and set-builder notation.

The following video describes: Set Notations, Empty Set, Symbols for “is an element of’ subset, intersection and union.

Set Notation: Roster Method, Set Builder Notation.



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