Sets

A set is a collection of distinct elements.

Constants

Symbol	Notation	Definition
`EmptySet`	\( \varnothing \) or \( \emptyset \)

Functions

New sets can be defined using a set expression. A set expression is an expression with one of the following head functions.

Function	Operation
`CartesianProduct`	\[ \operatorname{A} \times \operatorname{B} \]	A.k.a the product set, the set direct product or cross product. Q173740
`Complement`	\[ \operatorname{A}^\complement \]	The set of elements that are not in \( \operatorname{A} \). If \(\operatorname{A}\) is a numeric domain, the universe is assumed to be the set of all numbers. Q242767
`Intersection`	\[ \operatorname{A} \cap \operatorname{B} \]	The set of elements that are in \(\operatorname{A}\) and in \(\operatorname{B}\) Q185837
`Union`	\[ \operatorname{A} \cup \operatorname{B} \]	The set of elements that are in \(\operatorname{A}\) or in \(\operatorname{B}\) Q173740
`Set`	\(\lbrace 1, 2, 3 \rbrace \)	Set builder notation
`SetMinus`	\[ \operatorname{A} \setminus \operatorname{B} \]	Q18192442
`SymmetricDifference`	\[ \operatorname{A} \triangle \operatorname{B} \]	Disjunctive union = \( (\operatorname{A} \setminus \operatorname{B}) \cup (\operatorname{B} \setminus \operatorname{A})\) Q1147242

Relations

Function
`Element`	\[ x \in \operatorname{A} \]
`NotElement`	\[ x \not\in \operatorname{A} \]
`NotSubset`	\[ A \nsubset \operatorname{B} \]
`NotSuperset`	\[ A \nsupset \operatorname{B} \]
`Subset`	\[ \operatorname{A} \subset \operatorname{B} \] \[ \operatorname{A} \subsetneq \operatorname{B} \] \[ \operatorname{A} \varsubsetneqq \operatorname{B} \]
`SubsetEqual`	\[ \operatorname{A} \subseteq \operatorname{B} \]
`Superset`	\[ \operatorname{A} \supset \operatorname{B} \] \[ \operatorname{A} \supsetneq \operatorname{B} \] \[ \operatorname{A} \varsupsetneq \operatorname{B} \]
`SupersetEqual`	\[ \operatorname{A} \supseteq \operatorname{B} \]