Set theory symbols

 

Set theory symbols

 

Set theory symbols with Symbol Name , Meaning and definition and also with Example:                                                             

                              

 

 

Symbol	Symbol Name	Meaning / Definition	Example
∩	Intersection	Set of elements common to both sets A and B	A ∩ B = {x : x ∈ A and x ∈ B}
∪	Union	Set of elements in either set A or set B (or both)	A ∪ B = {x : x ∈ A or x ∈ B}
⊆	Subset	Set A is included in set B	{1, 2} ⊆ {1, 2, 3}
⊂	Proper Subset	Set A is a subset of B, but A ≠ B	{1, 2} ⊂ {1, 2, 3}
⊄	Not Subset	Set A is not a subset of set B	{1, 2} ⊄ {1, 2, 3}
⊇	Superset	Set A contains all elements of set B	{1, 2, 3} ⊇ {1, 2}
⊃	Proper Superset	Set A is a superset of B, but A ≠ B	{1, 2, 3} ⊃ {1, 2}
⊅	Not Superset	Set A is not a superset of set B	{1, 2, 3} ⊅ {1, 2, 4}
℘(A)	Power Set	Set of all subsets of set A	℘({1, 2}) = {∅, {1}, {2}, {1, 2}}
=	Equality	Sets have the same elements	{1, 2} = {2, 1}
symbol
¬A	Complement	Set of elements not in set A	¬{1, 2} = {3, 4, 5}
A \ B	Relative Complement	Set of elements in A but not in B	{1, 2, 3, 4} \ {3, 4, 5} = {1, 2}
A’	Complement	Same as ¬A	A’ = ¬A
A ∆ B	Symmetric Difference	Set of elements in either A or B, but not both	{1, 2, 3} ∆ {3, 4, 5} = {1, 2, 4, 5}
A ⊖ B	Symmetric Difference	Same as A ∆ B	A ⊖ B = A ∆ B
x ∈ A	Element of	Element x belongs to set A	3 ∈ {1, 2, 3}
x ∉ A	Not Element of	Element x does not belong to set A	4 ∉ {1, 2, 3}
(a, b)	Ordered Pair	Pair of elements (a, b)	(3, 4) is an ordered pair
A × B	Cartesian Product	Set of ordered pairs from sets A and B	{1, 2} × {3, 4} = {(1, 3), (1, 4), (2, 3), (2, 4)}
symbol
A	Cardinality	Vertical Bar	Such that (used in set-builder notation)
ℵ₀	Aleph-Null	Cardinality of countably infinite sets	ℵ₀ represents the size of ℕ (natural numbers)
ℵ₁	Aleph-One	Cardinality of the next larger infinite set	ℵ₁ represents a larger infinity
∅	Empty Set	Set with no elements	∅ ⊆ A for any set A
U	Universal Set	Set containing all possible elements	U = {x
ℕ	Natural Numbers (with 0)	Set of non-negative integers	ℕ = {0, 1, 2, 3, …}
ℕ*	Natural Numbers (no 0)	Set of positive integers	ℕ* = {1, 2, 3, …}
ℤ	Integer Numbers	Set of all integers	ℤ = {…, -3, -2, -1, 0, 1, 2, 3, …}
ℚ	Rational Numbers	Set of fractions a/b, where a and b are integers and b ≠ 0	ℚ = {x
ℝ	Real Numbers	Set of all real numbers	ℝ = {x
ℂ	Complex Numbers	Set of numbers in the form a + bi	ℂ = {z

Please note that the examples provided are for illustration purposes and might not cover all possible scenarios. Additionally, while these explanations are standard, there may be variations in notation and terminology in different contexts.

Symbol	Name	Meaning / Definition
∅	Empty Set	The set with no elements.
∈	Element of	An element belongs to a set.
∉	Not Element of	An element does not belong to a set.
⊆	Subset	A set is a subset of another set.
⊂	Proper Subset	A set is a subset of another set, but not equal.
⊄	Not Subset	A set is not a subset of another set.
⊇	Superset	A set contains all elements of another set.
⊃	Proper Superset	A set contains all elements of another set, but not equal.
⊅	Not Superset	A set is not a superset of another set.
∪	Union	The set of elements that belong to either of two sets.
∩	Intersection	The set of elements that belong to both sets.
∖	Set Difference	The set of elements in one set but not in another set.
∆	Symmetric Difference	The set of elements that belong to either set, but not both.
‘	Complement	The set of elements not in a given set.
		Cardinality
Symbol
∉	Not an Element of	An element does not belong to a set.
⊍	Double Superset	A set is a superset of another set, possibly equal.
⊏	Double Subset	A set is a subset of another set, possibly equal.
⊐	Double Superset	A set is a superset of another set, possibly equal.
⊑	Double Subset	A set is a subset of another set, possibly equal.
⊓	Meet (Lattice)	The infimum (greatest lower bound) of two sets in a lattice.
⊔	Join (Lattice)	The supremum (least upper bound) of two sets in a lattice.
⊢	Entails	A logical relationship indicating that a statement is a logical consequence of another.
⊣	Left Tack	Used in categorical mathematics to denote the left adjoint of a functor.
⊤	Top	The universal set or the largest element in a lattice.
⊥	Bottom	The empty set or the smallest element in a lattice.
⟦…⟧	Iverson Bracket	A notation used to indicate the truth value of a logical expression.
∀	For All	Universal quantification, “for all” or “for every”.
∃	Exists	Existential quantification, “there exists” or “there is”.
∄	Does Not Exist	Denotes that there does not exist an element satisfying a certain property.
⟹	Implies	Implies or implies that.
⟺	If and Only If	Logical biconditional or equivalence.

Please note that this is not an exhaustive list, but it includes many of the commonly used

 

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