Set Theory Symbols

List of set symbols of set theory and probability.

Table of set theory symbols

Symbol	Symbol Name	Meaning / definition	Example
{ }	set	a collection of elements	A={3,7,9,14}, B={9,14,28}
A ∩ B	intersection	objects that belong to set A and set B	A ∩ B = {9,14}
A ∪ B	union	objects that belong to set A or set B	A ∪ B = {3,7,9,14,28}
A ⊆ B	subset	subset has less elements or equal to the set	{9,14,28} ⊆ {9,14,28}
A ⊂ B	proper subset / strict subset	subset has less elements than the set	{9,14} ⊂ {9,14,28}
A ⊄ B	not subset	left set not a subset of right set	{9,66} ⊄ {9,14,28}
A ⊇ B	superset	set A has more elements or equal to the set B	{9,14,28} ⊇ {9,14,28}
A ⊃ B	proper superset / strict superset	set A has more elements than set B	{9,14,28} ⊃ {9,14}
A ⊅ B	not superset	set A is not a superset of set B	{9,14,28} ⊅ {9,66}
2A	power set	all subsets of A
Ƥ (A)	power set	all subsets of A
A = B	equality	both sets have the same members	A={3,9,14}, B={3,9,14}, A=B
Ac	complement	all the objects that do not belong to set A
A \ B	relative complement	objects that belong to A and not to B	A={3,9,14},     B={1,2,3}, A-B={9,14}
A - B	relative complement	objects that belong to A and not to B	A={3,9,14},     B={1,2,3}, A-B={9,14}
A ∆ B	symmetric difference	objects that belong to A or B but not to their intersection	A={3,9,14},     B={1,2,3}, A ∆ B={1,2,9,14}
A ⊖ B	symmetric difference	objects that belong to A or B but not to their intersection	A={3,9,14},     B={1,2,3}, A ⊖ B={1,2,9,14}
a∈A	element of	set membership	A={3,9,14}, 3 ∈ A
x∉A	not element of	no set membership	A={3,9,14}, 1 ∉ A
(a,b)	ordered pair	collection of 2 elements
A×B	cartesian product	set of all ordered pairs from A and B
|A|	cardinality	the number of elements of set A	A={3,9,14}, |A|=3
#A	cardinality	the number of elements of set A	A={3,9,14}, #A=3
א	aleph	infinite cardinality
Ø	empty set	Ø = { }	C = {Ø}
U	universal set	set of all possible values
ℕ0	natural numbers set (with zero)	ℕ0 = {0,1,2,3,4,...}	0 ∈ ℕ0
ℕ1	natural numbers set (without zero)	ℕ1 = {1,2,3,4,5,...}	6 ∈ ℕ1
ℤ	integer numbers set	ℤ = {...-3,-2,-1,0,1,2,3,...}	-6 ∈ ℤ
ℚ	rational numbers set	ℚ = {x | x=a/b, a,b∈ℕ}	2/6 ∈ ℚ
ℝ	real numbers set	ℝ = {x | -∞ < x <∞}	6.343434 ∈ ℝ
ℂ	complex numbers set	ℂ = {z | z=a+bi, -∞<a<∞,      -∞<b<∞}	6+2i ∈ ℂ

 

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See also

• Probability & statistics symbols
• Basic math symbols
• Logic symbols
• Probability & statistics