Set Theory Symbols

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 \(2^{s}\), s is number of elements in set C

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 A-B 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) \(\mathbb{N}\)1 = {1,2,3,4,5,…} 6 ∈ \(\mathbb{N}\)1
\(\mathbb{N}\)0 natural numbers / whole numbers  set (with zero) \(\mathbb{N}\)0 = {0,1,2,3,4,…} 0 ∈ \(\mathbb{N}\)0
\(\mathbb{Q}\) rational numbers set \(\mathbb{Q}\)= {x | x=a/b, a,b∈\(\mathbb{Z}\)} 2/6 ∈ \(\mathbb{Q}\)
\(\mathbb{Z}\) integer numbers set \(\mathbb{Z}\)= {…-3,-2,-1,0,1,2,3,…} -6 ∈ \(\mathbb{Z}\)
\(\mathbb{C}\) complex numbers set \(\mathbb{C}\)= {z | z=a+bi, -∞<a<∞,                         -∞<b<∞} 6+2i ∈ \(\mathbb{C}\)
\(\mathbb{R}\) real numbers set \(\mathbb{R}\)= {x | -∞ < x <∞} 6.343434 ∈\(\mathbb{R}\)<

Practise This Question

Solve the equation 5x312=1. The value of x is