## Set Symbols

**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:

{2, 4, 6, 8, … }

Three dots means goes on forever (infinite)

Table of Contents

## Common Symbols Used in Set Theory

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

In the examples C = {0,1,2,3,4} and D = {3,4,5,6}

Symbol | Meaning | Example |

{ } | Set: a collection of elements | {0,1,2,3,4} |

A ∪ B | Union: in A or B (or both) | C ∪ D = {0,1,2,3,4,5,6} |

A ∩ B | Intersection: in both A and B | C ∩ D = {3,4} |

A ⊆ B | Subset: A has some (or all) elements of B | {3,4,5,6} ⊆ D |

A ⊂ B | Proper Subset: A has some elements of B | {3,6} ⊂ D |

A ⊄ B | Not a Subset: A is not a subset of B | {0,1} ⊄ D |

A ⊇ B | Superset: A has same elements as B, or more | {0,1,2} ⊇ {0,1,2} |

A ⊃ B | Proper Superset: A has B’s elements and more | {0,1,2,3} ⊃ {1,2,3} |

A ⊅ B | Not a Superset: A is not a superset of B | {1,2,6} ⊅ {1,9} |

A^{c} | Complement: elements not in A | D^{c} = {1,2,6,7}When = {1,2,3,4,5,6,7} |

A − B | Difference: in A but not in B | {0,1,2,3} − {3,4} = {0,1,2} |

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} |

∅ | 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, x^{2}>x |

∃ | There Exists | ∃ x | x^{2}>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 |