Set Notation
Set notation refers to the different symbols used in the representation and operation of sets. The set notation used to represent the elements of sets is curly brackets i.e., {}.
In this article, we will explore set notation, set notations for set representation and set operations. We will also cover the set notation table and solve some examples related to set notation.
Table of Content
- What is Set Notation?
- Set Notation for Set Representation
- Set Notation for Set Operations
- Set Notation for Set Operations Table
- Set Notation Table
- Examples on Set Notation
What is Set Notation?
Set notations are the symbols used to represent the sets and operations on the sets. Different types of set notations are used in set theory. The set notation is used in every set like curly braces, commas, colons, unions, intersections, set differences and many more.
Set Notation for Set Representation
The different set notations for set representation include curly brackets, colon, belongs to, not belongs to, universal, and empty set.
Set Notation for Set Representation |
Symbol |
Description |
---|---|---|
Curly Brackets |
{} |
The curly brackets are used to represent a set. An example includes set A = {1, 2, 3}. |
Comma |
, |
The comma is used to separate the elements of the sets. |
Colon |
: |
It is used in the set-builder representation of a set. For example, S = {x: x is an even number} |
Element of |
∈ |
It represents that an element belongs to the set. A = {1, 2} then 1∈ A. |
Not Element of |
∉ |
It represents that an element does not belong to a set. A = {2} then 1 ∉ A. |
Universal Set |
U |
It represents the universal set of a set |
Empty set |
Φ |
It represents the empty set. |
Set Notation for Set Operations
Different set notation for set operations include union, intersection, subset, difference, symmetric difference and complement of sets.
Union
Union (U) is represented by ∪ set notation. Union is a binary operations on two sets that includes all the elements of both sets. It is mathematically represented as for two sets A and B, A ∪ B = {x: x∈A or x∈B}.
Example: Find the union of set X = {2, 3, 4} and Y = {4, 5, 6}.
Solution:
X = {2, 3, 4}
Y = {4, 5, 6}
X ∪ Y = {2, 3, 4, 5, 6}
Intersection
Intersection (∩) is represented by ∩ set notation. Intersection is a binary operation on two sets that includes the common elements of both sets. It is mathematically represented as for two sets A and B, A ∩ B = {x: x∈A and x∈B}.
Example: Find the intersection f set X = {2, 3, 4} and Y = {4, 5, 6}.
Solution:
X = {2, 3, 4}
Y = {4, 5, 6}
X ∩ Y = {4}
Difference
Difference ( \ ) is represented by \, – set notation. Difference is a binary operation on two sets that includes elements of first set that are not present in second set. It is mathematically represented as for two sets A and B, A – B = {x: x∈A and x∉B}.
Example: Find the difference of set X = {2, 3, 4} and Y = {4, 5, 6}.
Solution:
X = {2, 3, 4}
Y = {4, 5, 6}
X – Y = {2, 3}
Subset
The subset of set is represented by ⊆ set notation. The set B is called the subset of A if all the elements of set B are present in set A. It is mathematically represented as for two sets A and B, B ⊆ A = {x: x∈A ∀ x∈B}.
Example: Find whether X is subset of Y or not where set X = {2, 3, 4} and Y = {2, 3, 4, 5, 6}.
Solution:
X = {2, 3, 4}
Y = {2, 3, 4, 5, 6}
Since Y includes all the elements of X
Therefore, X ⊆ Y
Complement
Complement (A’) of set is represented by (Set)c set notation. Complement of a set includes the elements of universal set that is not present in the given set. It is mathematically represented as for a set A Ac = {x: x∉A}.
Example: Find the complement of set X = {2, 3, 4} and U = {2, 3, 4, 5, 6}.
Solution:
X = {2, 3, 4}
Xc = {5, 6}
Set Notation for Set Operations Table
The table below represents different set notations used for set operations.
Set Notation for Set Operations |
Symbol |
Description |
---|---|---|
Union |
∪ |
The union of two sets includes all elements present in both sets. |
Intersection |
∩ |
The intersection of two sets includes common elements between two sets. |
Complement |
c |
The complement of set is given by U – set. |
Set Difference |
– |
The set difference of two sets includes the elements of first set that are not present in second set. |
Subset |
⊆ |
The subset of a set is the set that includes some element of a set. |
Set Notation Table
Table below represents the different set notations.
Set Notation |
Set Notation Name |
---|---|
{} |
Curly Brackets |
: |
Colon |
∈ |
Belongs to |
∉ |
Not belongs to |
U |
Universal set |
Φ |
Empty set |
⊂ |
Proper Subset |
⊆ |
Subset |
∪ |
Union |
∩ |
Intersection |
– |
Set difference |
Δ |
Symmetric difference |
A’ |
Complement of set A |
Articles Related to Set Notation:
Examples on Set Notation
Example 1: Find the intersection fo set P = {1, 3, 5} and Q = {2, 5, 8}.
Solution:
P = {1, 3, 5}
Q = {2, 5, 8}
P ∩ Q = {5}
Example 2: Find the union of set P = {5, 10} and Q = {12, 15, 18}.
Solution:
P = {5, 10}
Q = {12, 15, 18}
P ∪ Q = {5, 10, 12, 15, 18}
Example 3: Find the difference of set P = {1, 3, 5} and Q = {2, 5, 8}.
Solution:
P = {1, 3, 5}
Q = {2, 5, 8}
P – Q = {1, 3}
Example 4: Find the complement of set X = {a, b, d} and U = {a, b, c, d, e}.
Solution:
X = {a, b, d}
Xc = {c, e}
Example 5: Find whether P is subset of Q or not where set P = {2, 4} and Q = {4, 5, 6}.
Solution:
P = {2, 4}
Q = {4, 5, 6}
Since Q does not includes all the elements of P (element 2)
Therefore, P is not a subset of Q.
Practice Questions on Set Notation
Q1. Find the union of two sets A ={6, 4} and B = {3, 10}.
Q2. Find the intersection of two sets A = {5, 13} and B = {3, 13}.
Q3. Find the set difference A – B where, A = {12, 14, 16} and B = {8, 10, 13}.
Q4. Find whether B is subset of A or not where A = {a, b, c} and B = {a, b}
Q5. Find the complement of set A given A = {2, 4} and U = {1, 2, 3, 4, 5}.
FAQs on Set Notation
What Does ⊂ Mean in Set Notation?
In set notation, ⊂ means proper subset.
What Does ∪ and ∩ Mean in Math?
The ∪ means union and ∩ means intersection in Math.
What is Symbol for Set Notation?
The symbol for set notation is {}.
What is ∈?
∈ is the belongs to set notation which is used to represent if an element belongs to some set.
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