Set Notation
Set notation refers to the different symbols used in the process of working within and across the sets. The simplest set notation used to represent the elements of a set is the curly brackets { }. An example of a set is A = {a, b, c, d}. Here the set is represented with a capital letter, and its elements are denoted by small letters.
Set notation can be broadly classified as for set representation and for set operations. The set representation notations are μ  universal set, Ø  null set, ⊂  subset:, ∈  belongs to, A'  complement of a set. And the set notations for operations across sets are U  union, ∩  intersection,  difference, Δ  Delta. Let us learn more about the various set notations, with the help of examples, FAQs.
1.  What Is Set Notation? 
2.  Set Notation For Set Representation 
3.  Set Notation For Set Operations 
4.  Examples On Set Notation 
5.  Practice Questions 
6.  FAQs On Set Notation 
What Is Set Notation?
Set notations are the basic symbols used to denote the various representations across set operations. Set notation is used to denote any working within and across the sets. All the symbols except the number elements can be easily considered as the notations for sets. The simplest set notation is the Curley brackets, which are used to enclose and represent the elements of the set. The elements of a set are written using flower brackets { }, or by using parenthesis ( ).
The elements of a set are written and separated by commas. For example, set A containing the five vowels of the English alphabets is written as A = {a, e, i, o, u}. The sets are denoted by capital letters and the elements of the set are denoted by small letters.Set notation is further used to represent various sets and operations. Further, it is possible to represent the various relations and functions across sets, only with the help of set notation.
Broadly the set notations can be classified for set representations and for set operations. Let us now study in detail, the set notation for set representation, and the set formation for set operations.
Set Notation For Set Representation
Set notation used to generally represent some of the common sets are the universal set, empty set, the complement of a set. Further, we use special symbols of subset and belongs to, to relate the elements or the set itself, to another set.
 μ  Universal Set: This includes all the elements of all the sets which are being considered for set operations. If there is a set A of consonants, and set B of consonants, then μ  universal set represents all the english alphabets. Hence a universal set can be called a set that includes all the elements of all the sets under consideration.
 Ø  Null Set: A set that does not have any elements in it is referred to as a null set. It is also called an empty set and is represented as Ø = { }.
 A'  Complement Of A Set: The complement of a set is all the elements of the universal set, except the elements of the set A. For a set A, its complement is A' = μ  A. If the set A = {2, 3, 4, 5} , and μ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then A' = μ  A = {1, 6, 7, 8, 9, 10}.
 ⊂  Subset: The subset symbol is used to represent a set formed by taking a few elements of a given set. For a set A = {a, b, c, d, e}, if a new set B = {b, c, d} is formed by taking a few elements of set A, then we say that B is a subset of A, and this is denoted as B ⊂ A. Since there are fewer elements in set B, compared to set A, then B is called the proper subset of A. Also if B had equal or same elements of set A, then it would be denoted as B ⊂ A.
 ∈  Belongs to: This symbol '∈' is used, if a particular element is said to be belonging to a set A. If the set A = {a, b, c}, then we refer that the element a belongs to set A, as a ∈ A. And if a particular element d does not belong to the set A, then we denote it as d ∉ set A. The symbol ∉ means that it does not belong to the set.
Set Notation For Set Operations
Set notation help in conducting various operations across sets. The operations of union, intersection, difference, delta, across two or more sets are denoted by the various set notations, using symbols.
 U  Union of Sets: This operation of union of sets combines all the elements of the two sets and presents it as a single set. Here the common elements of the sets are written only once in the final union set. For two sets A = {a, b, c, d}, and B = {c, d, e}, we have A U B = { a, b, c, d, e}. The elements in the union set has more elements than in the individual sets.
 ∩  Intersection of Sets: The operation of intersection of sets takes the common elements of the two sets to form a new set. For the sets A = {a, b, c, d, e, f}, B = {e, f, g, h, i}, we have A ∩ B = {e, f}. Here we have taken the common elements and the number of elements in the intersection set is lesser than the elements in the individual sets.
  Difference: The difference of the two sets uses the same symbol of subtraction. Here the elements remaining after removing the common elements from the given set give the difference between the two sets. For the sets A = {a, b, c, d, e}, B = {b, c, d}, we have the difference of sets, between the sets A  B = A  (A ∩ B) = {a, b, c, d, e}  {b, c, d} = {a. e}.
 A'  Complement: For a set A, its complement is written as A' or A^{c}. The complement of a set is the set obtained after removing the given set elements from the universal set and taking the remaining elements. The formula for the complement of a set is A' = μ  A.
 Δ  Delta: The notation of delta between two sets gives the elements remaining after removing the common elements from the union of the two sets. For two sets A, and B we have A Δ B = (A U B)  (A ∩ B), Or A Δ B = (A  B) U (B  A). Also the A Δ B takes the elements of only set A and only set B.
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Examples of Set Notation

Example 1: Find the set notation used to represent the elements of only A, among the two sets A, and B?
Solution:
The set only A is written as A  B, and represents the elements which are in the set A, and which are not common to both the sets.
Only A = A  Common elements of set A and set B
A B = A  (A ∩ B)
Thus the set notation for only A is A B = A  (A ∩ B).

Example 2: Using set notation express the different formulas used to represent A Δ B.
Solution:
Here A Δ B represents the elements that are available in only set A, or only set B.
A Δ B = Elements of only set A or only set B
A Δ B = (only A) U (only B)
A Δ B = (A  B) U (B  A)
Another representation of A Δ B is all the elements of set A and set B, except the common elements of the sets A and B.
A Δ B = (AUB)  (A ∩B)
Thus using set notation we have A Δ B = (A  B) U (B  A) and A Δ B = (AUB)  (A ∩B).
FAQs on Set Notation
What Is Set Notation In Maths?
Set notations are the basic symbols used for the various representations across sets. Set notation for representing the elements of a set are the curly brackets { }. Generally, a set A = {a, b, c, d}, and here we represent the set using capital alphabets and its elements using small alphabets. Broadly set notations have been used for set representation and for set operations.
What Is Set Notation In Probability?
The set notation in probability represents all the possible outcomes/events of an experiment in a set. The outcomes on rolling two dice are represented using set notation, A = {(H, T), (T, H), (T, T), (H, H)}. And the set notation representing the outcome on rolling dice is S = {1, 2, 3, 4, 5, 6}.
What Are The Set Notations Used For Representing Different Sets?
The various set notations used for representing different types of sets is, μ  universal set, Ø  empty set(Null set), ⊂  subset, A'  complement of a set.
What Are The Set Notations For Operations Across Sets?
The various set notations used for operations across two sets is U  Union, ∩  Intersection,  Difference, Δ  Delta, A'  Complement.
How Do You Write Set Notation?
The set notation is generally written using symbols between the sets for set operations, and certain symbols for representing some special kind of sets. The set notation for the union of sets is A U B, for the intersection of sets is A ∩ B. And the set notation for representing some important sets is the μ  universal set, Ø  null set.
What Are the Types Of Set Notations For Representing Elements?
The two important types of set notations for representing the elements are the roster form and the set builder form. The set builder notation represents the elements of a set in the form of a sentence or mathematical expression, and the set builder form represents the elements by writing the elements distinctly. The set builder form of set notation is A = {x / x ∈ First five even number}, and the roster of of the same set is A = }2, 4, 6, 8, 10}.
Which Is The Best Form Of Set Notation For Writing A Set?
The best form of set notation is the notation which helps to easily represent the elements of a set. The roster form of set notation makes a simple listing of elements of a set and is the best form of set notation. The roster form of set notation to represent a set of English alphabet vowels is A = {a, e, i, o, u}.
Where Do You Use Set Notation?
The set notation is used to represent some of the important sets such as μ  universal set, Ø  null set, or to represent ⊂  subset. Also, the set notation is useful to represent the various set operations such as U  union of sets, ∩  intersection of sets,  difference of sets.
Give A Few Examples Of Set Notation.
Some of the important examples of set notations is μ  universal set, Ø  null set, U  union of sets, ∩  intersection of sets.
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