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.
| Sets & Set Notations | ||
|---|---|---|
| Set Notations | Sets Video Lessons | Set Worksheets |
Set Notations
Set theory is a branch of mathematics that deals with collections of objects called sets. To precisely describe relationships and operations within set theory, a specific set of symbols is used.
The following table gives a summary of the symbols use in sets.
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”
⊆ denotes “is a subset of”.
⊂ denotes “is a proper subset of”.
⊈ denotes “is not a subset of”.
∪ denotes “union”.
∩ denotes “intersection”.
⊇ denotes “is a superset of”.
⊃ denotes “is a proper superset of”.
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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