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Mathematical Symbols are very important to learn mathematics, on using symbols we can easily understand the concepts of topics.
Mathematical Symbols can be categorized on their importance in the following ways:
- Mathematics symbols - Number
- Mathematics symbols - Basic
- Mathematics symbols - Algebraic
- Mathematics symbols - Geometric
- Mathematics symbols - Trigonometry
- Mathematics symbols - Set Theory
- Mathematics symbols - Statistics & Probability
- Mathematics symbols - Calculus And Analysis
- Mathematics symbols - Logical
- Mathematics symbols - Roman
- Mathematics symbols - Greek
- Mathematics symbols - Miscellaneous
Now we shall learn /discuss Sixth topic Mathematics symbols - Set Theory on this post.
Mathematical symbols - Set Theory
These are very important Basic Tools frequently used by us in Particular topics of algebra like Sets and relations, Pure Algebra, Mathematical Logics as well as in other branches of applied mathematics and sciences.
Set can be written by capital alphabets like A, B, C, P, Q, X, Y, etc and it can be written in Curley Brackets.
S.N.
Symbol
Name
of Symbol
Definition
Illustration
1
{ }
Set
A well-defined collection of objects
/ elements are known as a set.
A = {1,17,19,24},
2
A = B
equality
both sets have the same members (orders
may be different)
A = {1,2,3,4}
3
A ∪ B
union
Those objects which belong to set A
or set B.
If A = {1,17,19,24}, and
4
A ∩ B
intersection
Those objects that belong to set A
and set B both.
If A = {1,17,19,24}, and
5
A ⊆ B
subset
A is a subset of B or set A is
included in set B.
{1,2,3,4} ⊆ {1,2,3,4}
6
P ⊂ Q
proper subset or a strict subset
“P is a subset of Q, but Pis not
equal to Q”.
{1,2, 4} ⊂ {1,2,3,4}
7
P ⊄ Q
not a subset
"The first (P) set is not a subset of another or second (Q ) set "
{1,2, 4} ⊄ {1,22, 44}
8
P ⊇ Q
superset
P is a superset of Q or set P
includes set Q
{1,14,28} ⊇ {1,14}
9
P ⊅ Q
not a superset
set P is not a superset of set Q
{19,14,208} ⊅ {19,23}
10
power set
All subsets of any set like A
11
P (A)
power set
All subsets of any set like A
12
complement
All the objects that do not belong
to given set A
13
complement
All the objects that do not belong
to given set A
14
A – B
Set A-minus Set B
Objects that belong to set A and but
not to set B
If A = {1,2,3,4} and
15
A / B
Set A minus Set B
Objects that belong to set A and but
not to set B
If A = {1,2,3,4} and
16
B – A
Set B minus Set A
Or
relative complement
Objects that belong to set B and but
not to set A
If A = {1,2,3,4} and
17
B / A
Set B minus Set A
Objects that belong to set B and but
not to set A
If A = {1,2,3,4} and
18
a ∈ A
belongs to
Element is member of a given set
If A = {1,2,3,4}
19
a ∉ A
Not belongs to OR
Element is NOT a member of given
set
If A = {1,2,3,4}
20
A ∆ B
Symmetric difference of sets
Set of all those elements that belong to A or B but
not to their intersection.
(A ∪ B) – (A ∩ B)
OR
If A = {1,2,3,4}
21
A ⊖ B
Symmetric difference of sets
Set of all those elements that belong to A or B but
not to their intersection.
If A = {1,2,3,4}
22
(x, y)
Ordered Pair of x and y
Set of two elements whose order is
fixed.
23
A × B
Cartesian Product
it is a set of all possible ordered pairs from A and
B
24
B × A
Cartesian Product
Set of all ordered pairs from B and
A
25
n (A)
The cardinality of set A
The total number of elements of the set
A
A = {1, 2,3,9,14},
26
|A|
The cardinality of set A
The total number of elements of the set
A
A = {1, 2,3,9,14}, |A|=5
27
(Phi)
Empty Set
The set having No elements.
28
(Zeta)
Universal Set
Superset of all sets
On having knowledge of the above Mathematics symbols - Set Theory we can easily enhance our subject ideas.
These are very important Basic Tools frequently used by us in Particular topics of algebra like Sets and relations, Pure Algebra, Mathematical Logics as well as in other branches of applied mathematics and sciences.
Set can be written by capital alphabets like A, B, C, P, Q, X, Y, etc and it can be written in Curley Brackets.
S.N.
|
Symbol
|
Name
of Symbol
|
Definition
|
Illustration
|
1
|
{ }
|
Set
|
A well-defined collection of objects
/ elements are known as a set.
|
A = {1,17,19,24},
B = {3, 7,19,24}, OR
C= Set of word MATHEMATICS
= {M, A, T, H, E, I, C, S}
|
2
|
A = B
|
equality
|
both sets have the same members (orders
may be different)
|
A = {1,2,3,4}
and
B = {1,2,3,4}
|
3
|
A ∪ B
|
union
|
Those objects which belong to set A
or set B.
|
If A = {1,17,19,24}, and
B = {3, 7,19,24}, then A ∪ B =
{1, 3, 7, 17, 19, 24}
|
4
|
A ∩ B
|
intersection
|
Those objects that belong to set A
and set B both.
|
If A = {1,17,19,24}, and
B = {3, 7,19,24}, then A ∩ B = {19,24}
|
5
|
A ⊆ B
|
subset
|
A is a subset of B or set A is
included in set B.
|
{1,2,3,4} ⊆ {1,2,3,4}
|
6
|
P ⊂ Q
|
proper subset or a strict subset
|
“P is a subset of Q, but Pis not
equal to Q”.
|
{1,2, 4} ⊂ {1,2,3,4}
|
7
|
P ⊄ Q
|
not a subset
|
"The first (P) set is not a subset of another or second (Q ) set "
|
{1,2, 4} ⊄ {1,22, 44}
|
8
|
P ⊇ Q
|
superset
|
P is a superset of Q or set P
includes set Q
|
{1,14,28} ⊇ {1,14}
|
9
|
P ⊅ Q
|
not a superset
|
set P is not a superset of set Q
|
{19,14,208} ⊅ {19,23}
|
10
|
 |
power set
|
All subsets of any set like A
|
|
11
|
P (A)
|
power set
|
All subsets of any set like A
|
|
12
|
 |
complement
|
All the objects that do not belong
to given set A
|
|
13
|
 |
complement
|
All the objects that do not belong
to given set A
|
|
14
|
A – B
|
Set A-minus Set B
Or
relative complement
|
Objects that belong to set A and but
not to set B
|
If A = {1,2,3,4} and
B = {1, 2, 5, 7}
then
A-B =
{3, 4}
|
15
|
A / B
|
Set A minus Set B
or
relative complement
|
Objects that belong to set A and but
not to set B
|
If A = {1,2,3,4} and
B = {1, 2, 5, 7}
then
A-B =
{3, 4}
|
16
|
B – A
|
Set B minus Set A
Or
relative complement
|
Objects that belong to set B and but
not to set A
|
If A = {1,2,3,4} and
B = {1, 2, 5, 7}
then
B- A = {5, 7}
|
17
|
B / A
|
Set B minus Set A
or
relative complement
|
Objects that belong to set B and but
not to set A
|
If A = {1,2,3,4} and
B = {1, 2, 5, 7}
then
B- A = {5, 7}
|
18
|
a ∈ A
|
belongs to
OR
elements of
|
Element is member of a given set
|
If A = {1,2,3,4}
then
1 ∈ A, 2 ∈ A,
3 ∈ A, 4 ∈ A
|
19
|
a ∉ A
|
Not belongs to OR
not element of
|
Element is NOT a member of given
set
|
If A = {1,2,3,4}
then
5 ∉ A
|
20
|
A ∆ B
|
Symmetric difference of sets
|
Set of all those elements that belong to A or B but
not to their intersection.
(A ∪ B) – (A ∩ B)
OR
(A - B) ∪ (B - A)
|
If A = {1,2,3,4}
and
B = {1, 2, 5, 7}
then
A ∆ B = {3,4,5,7}
|
21
|
A ⊖ B
|
Symmetric difference of sets
|
Set of all those elements that belong to A or B but
not to their intersection.
(A ∪ B) – (A ∩ B)
OR
(A - B) ∪ (B - A)
|
If A = {1,2,3,4}
and
B = {1, 2, 5, 7}
then
A ⊖ B = {3,4,5,7}
|
22
|
(x, y)
|
Ordered Pair of x and y
|
Set of two elements whose order is
fixed.
|
|
23
|
A × B
|
Cartesian Product
|
it is a set of all possible ordered pairs from A and
B
|
|
24
|
B × A
|
Cartesian Product
|
Set of all ordered pairs from B and
A
|
|
25
|
n (A)
|
The cardinality of set A
|
The total number of elements of the set
A
|
A = {1, 2,3,9,14},
n(A) =5
|
26
|
|A|
|
The cardinality of set A
|
The total number of elements of the set
A
|
A = {1, 2,3,9,14}, |A|=5
|
27
|
|
Empty Set
|
The set having No elements.
|
|
28
|
 |
Universal Set
|
Superset of all sets
|
___________________________________________________________
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