Set Symbols (original) (raw)

Last Updated : 11 May, 2026

Set symbols are special mathematical symbols used in set theory. These symbols help to describe relationships between sets, elements, and operations involving sets.

Some of the commonly used set symbols:

The symbols used in number systems are included in the table below:

Symbol Name Meaning/Definition Example
W **Whole Numbers Non-negative integers including zero. We know W = {1, 2, 3, 4, 5, . . . }0 ∈ W
N or ℕ **Natural Numbers Natural numbers are sometimes referred to as counting numbers that begin with 1. We know N = {1, 2, 3, . . . }1 ∈ N
Z or ℤ **Integers Integers are comparable to whole numbers, except that they also include negative values. We know Z = {. . . , -3, -2, -1, 0, 1, 2, 3 . . .}-6 ∈ Z
Q or ℚ **Rational Numbers Rational numbers are those that are stated as a/b. In this case, a and b are integers with b ≠ 0. Q = {x | x = a/b, a, b ∈ Z and b ≠ 0}2/6 ∈ Q
P or ℙ **Irrational Numbers Those number which can't be represented in the form of a/b, are called irrational number i.e., all real number which are not rational. P = {x | x ∉ Q}π, e ∈ P
R or ℝ **Real Numbers Whole numbers, rational numbers, and irrational numbers make up real numbers. R = {x | -∞ < x <∞}6.343434 ∈ R
C or ℂ **Complex Numbers A complex number is a combination of a real number and an imaginary number. C = {z | z = a + bi, a, b ∈ R}6 + 2__i_ ∈ C

**Basic Set Notation

Delimiters are special characters or sequences of characters that indicate the beginning or end of a certain statement or function body of a specified set. The following are the delimiters set theory symbols and meanings:

Symbol Name Meaning/Definition Example
{} **Set Within these brackets is a bunch of elements/ numbers/ alphabets in a set. {15, 22, c, d}
| **Such that These are used to construct a set by specifying what is contained within it. { q | q > 6}The statement specifies the collection of all q's such that q is bigger than 6.
: **Such that The ":" symbol is sometimes used instead of the "|" symbol. The above sentence can alternatively be written as {q : q > 6}.

**Relational Symbols in Sets Theory

Set theory symbols are used to identify a specific set as well as to determine/show a relationship between distinct sets or relationships inside a set, such as the relationship between a set and its constituent. The table below depicts such relationship symbols, along with their meanings and examples:

Symbol Name Meaning/Definition Example
a ∈ A **Is a Component of This specifies that an element is a member of a specific set. If a set A = {12, 17, 18, 27} we may say that 27 ∈ A
b ∉ B **Is not a Component of This indicates that an element does not belong to a particular set. If a set B = {c, d, g, h, 32, 54, 59} then any element other than the one in the set does not belong to this set. As an example, 18 ∉ B
A = B **Equality Relation The provided sets are equivalent in the sense that they have the same components. If you put P = {16, 22, a} and Q = {16, 22, a} then P = Q
A ⊆ B **Subset When all of the items of A are present in B, A is a subset of B. A = {31, b} and B={a, b, 31, 54}{31, b} ⊆ {a, b, 31, 54}
A ⊂ B **Proper Subset P is said to be a proper subset of B when it is a subset of B and not equal to B. A = {24, c} and B = {a, c, 24, 50} A ⊂ B
A ⊄ B **Not a Subset As a result, set A is not a subset of set B. A = {67, 52} and B = {42, 34, 12}A ⊄ B
A ⊇ B **Superset A is a superset of B if set B is a subset of A. Set A can be the same as or greater than Set B. A = {14, 18, 26} and B = {14, 18, 26} {14, 18, 26} ⊇ {14, 18, 26}
A ⊃ B **Proper Superset Set A has more elements than set B since it is a superset of B. {14, 18, 26, 42} ⊃ {18,26}
A ⊅ B **Not a Superset When all of the elements of B are not present in A, A is not a true superset of B. A = {11, 12, 16} and B = {11, 19}{11, 12, 16} ⊅ {11, 19}
Ø **Empty Set An empty or null set is one that does not include any elements. {22, y} ∩ {33, a} = Ø
U **Universal Set A set that contains elements from all relevant sets, including its own. If, A = {a, b, c} and B = {1, 2, 3, b, c}, then U = {1, 2, 3, a, b, c}
|A or n{A} **Cardinality of a Set Cardinality refers to the number of items in a particular collection.
P(X) **Power Set A power set is the set of all subsets of set X, including the set itself and the null set. If X = {12, 16, 19}P(X) = {12, 16, 19} = {{}, {12}, {16}, {19}, {12, 16}, {16, 19}, {12, 19}, {12, 16, 19}}

**Set Operations Symbols

With examples, we will study set theory symbols and meanings for numerous operations such as union, complement, intersection, difference, and others.

Symbol Name Meaning/Definition Example
A ∪ B **Union of Sets The union of sets creates an entirely new set by combining all of the components in the provided sets. A = {p, q, u, v, w}B = {r, s, x, y}A ∪ B (A union B) = {p, q, u, v, w, r, s, x, y}
A ∩ B **Intersection of Sets The common component of both sets is included in the intersection. A = { 4, 8, a, b} and B = {3, 8, c, b}, thenA ∩ B = {8, b}
Xc OR X' **Complement of a set A set's complement comprises all things that do not belong to the provided set. If A is universal set and A = {3, 6, 8, 13, 15, 17, 18, 19, 22, 24} and B = {13, 15, 17, 18, 19} thenX′ = A – B⇒ X′ = {3, 6, 8, 22, 24}
A − B **Set Difference The difference set is a set that contains items from one set that are not found in another. A = {12, 13, 15, 19} and B = {13, 14, 15, 16, 17}A - B = {12, 19}
A × B **Cartesian Product of Sets A Cartesian product is the product of the ordered components of the sets. A = {4, 5, 6} and B = {r}A × B = {(4, r), (5, r), (6, r)}
A ∆ B **Symmetric Difference of Sets A Δ B = (A - B) U (B - A) denotes the symmetric difference. A = {13, 19, 25, 28, 37},B = {13, 25, 55, 31}A ∆ B = { 19, 28, 37, 55, 31}