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Set Notation

Related Topics: More Lessons on Sets

These lessons are part of a series of 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.

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:
A = {1, 2, 3} = {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.
We can have infinite sets for example {1, 2, 3, ...}

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”

If A = {1, 3, 5} then 1 ∈ A and 2 ∉ A


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 ҩs an element ofҬ subset, intersection and union. Set Notation
Roster Method, Set Builder Notation.

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