Set theory was developed by mathematicians to be able to talk about collections of objects. It has turned out to be an invaluable tool for defining some of the most complicated mathematical structures.
Let us explore few common Set theory symbols used in more complicated math structures.
Consider a Universal set (U) = {1, 2, 7, 9, 13, 15, 21, 23, 28, 30}
Symbol 
Symbol Name 
Meaning / definition 
Example 
{ } 
set 
a collection of elements 
A = {1, 7, 9, 13, 15, 23}, B = {7, 13, 15, 21} 
A ∪ B 
union 
objects that belong to set A or set B 
A ∪ B = {1, 7, 9, 13, 15, 21, 23} 
A ∩ B 
intersection 
objects that belong to both the sets, A and B 
A ∩ B = {7, 13, 15 } 
A ⊆ B 
subset 
subset has few or all elements equal to the set 
{7, 15} ⊆ {7, 13, 15, 21} 
A ⊄ B 
not subset 
left set not a subset of right set 
{1, 23} ⊄ B 
A ⊂ B 
proper subset / strict subset 
subset has fewer elements than the set 
{7, 13, 15} ⊂ {1, 7, 9, 13, 15, 23} 
A ⊃ B 
proper superset / strict superset 
set A has more elements than set B 
{1, 7, 9, 13, 15, 23} ⊃ {7. 13. 15. } 
A ⊇ B 
superset 
set A has more elements or equal to the set B 
{1, 7, 9, 13, 15, 23} ⊃ {7. 13. 15. 21} 
Ø 
empty set 
Ø = { } 
C = {Ø} 
P (C) 
power set 
all subsets of C 
C = {4,7}, P(C) = {{}, {4}, {7}, {4,7}} Given by \(2^{s}\) 
A ⊅ B 
not superset 
set A is not a superset of set B 
{1, 7, 9, 13, 15, 23} ⊅{7, 13, 15, 21} 
A = B 
equality 
both sets have the same members 
{7, 13,15} = {7, 13, 15} 
A \ B or AB 
relative complement 
objects that belong to A and not to B 
{1, 9, 23} 
Ac 
complement 
all the objects that do not belong to set A 
We know, U = {1, 2, 7, 9, 13, 15, 21, 23, 28, 30} Ac = {2, 21, 28, 30} 
A ∆ B 
symmetric difference 
objects that belong to A or B but not to their intersection 
A ∆ B = {1, 9, 21, 23} 
a∈B 
element of 
set membership 
B = {7, 13, 15, 21}, 13 ∈ B 
(a,b) 
ordered pair 
collection of 2 elements 

x∉A 
not element of 
no set membership 
A = {1, 7, 9, 13, 15, 23, 5 ∉ A 
B, #B 
cardinality 
the number of elements of set B 
B = {7, 13, 15, 21}, B=4 
A×B 
cartesian product 
set of all ordered pairs from A and B 
{3,5} × {7,8} = {(3,7), (3,8), (5,7), (5, 8) } 
\(\mathbb{N}\) 
natural numbers / whole numbers set (without zero) 
\(\mathbb{N}\) 
6 ∈ \(\mathbb{N}\) 
\(\mathbb{N}\) 
natural numbers / whole numbers set (with zero) 
\(\mathbb{N}\) 
0 ∈ \(\mathbb{N}\) 
\(\mathbb{Q}\) 
rational numbers set 
\(\mathbb{Q}\) 
2/6 ∈ \(\mathbb{Q}\) 
\(\mathbb{Z}\) 
integer numbers set 
\(\mathbb{Z}\) 
6 ∈ \(\mathbb{Z}\) 
\(\mathbb{C}\) 
complex numbers set 
\(\mathbb{C}\) 
6+2i ∈ \(\mathbb{C}\) 
\(\mathbb{R}\) 
real numbers set 
\(\mathbb{R}\) 
6.343434 ∈\(\mathbb{R}\) 
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