Set Symbols

A set is a collection of things, usually numbers. We can list each element (or "member") of a set inside curly brackets like this:

Common Symbols Used in Set Theory

Symbols save time and space when writing. Here are the most common set symbols

In the examples C = {1, 2, 3, 4} and D = {3, 4, 5}

Symbol	Meaning	Example
{ }	Set: a collection of elements	{1, 2, 3, 4}
A ∪ B	Union: in A or B (or both)	C ∪ D = {1, 2, 3, 4, 5}
A ∩ B	Intersection: in both A and B	C ∩ D = {3, 4}
A ⊆ B	Subset: every element of A is in B.	{3, 4, 5} ⊆ D
A ⊂ B	Proper Subset: every element of A is in B, but B has more elements.	{3, 5} ⊂ D
A ⊄ B	Not a Subset: A is not a subset of B	{1, 6} ⊄ C
A ⊇ B	Superset: A has same elements as B, or more	{1, 2, 3} ⊇ {1, 2, 3}
A ⊃ B	Proper Superset: A has B's elements and more	{1, 2, 3, 4} ⊃ {1, 2, 3}
A ⊅ B	Not a Superset: A is not a superset of B	{1, 2, 6} ⊅ {1, 9}
Ac	Complement: elements not in A	Dc = {1, 2, 6, 7} When = {1, 2, 3, 4, 5, 6, 7}
A − B	Difference: in A but not in B	{1, 2, 3, 4} − {3, 4} = {1, 2}
a ∈ A	Element of: a is in A	3 ∈ {1, 2, 3, 4}
b ∉ A	Not element of: b is not in A	6 ∉ {1, 2, 3, 4}
Ø	Empty set = {}	{1, 2} ∩ {3, 4} = Ø
	Universal Set: set of all possible values (in the area of interest)
P(A)	Power Set: all subsets of A	P({1, 2}) = { {}, {1}, {2}, {1, 2} }
A = B	Equality: both sets have the same members	{3, 4, 5} = {5, 3, 4}
A×B	Cartesian Product (set of ordered pairs from A and B)	{1, 2} × {3, 4} = {(1, 3), (1, 4), (2, 3), (2, 4)}
|A|	Cardinality: the number of elements of set A	|{3, 4}| = 2
|	Such that	{ n | n > 0 } = {1, 2, 3,...}
:	Such that	{ n : n > 0 } = {1, 2, 3,...}
∀	For All	∀x>1, x2>x For all x greater than 1 x-squared is greater than x
∃	There Exists	∃ x | x2>x There exists x such that x-squared is greater than x
∴	Therefore	a=b ∴ b=a
	Natural Numbers	{1, 2, 3,...} or {0, 1, 2, 3,...}
	Integers	{..., −3, −2, −1, 0, 1, 2, 3, ...}
	Rational Numbers
	Algebraic Numbers
	Real Numbers
	Imaginary Numbers	3i
	Complex Numbers	2 + 5i