Mathematical logic and foundations Definition

Complement

Definition

Let $U$ be a universal set and let $A$ be a subset of $U$ . The complement of $A$ in $U$ is the set $A^{c} = \{x \in U \mid x \notin A\}.$

Remarks

Other notations are $\overline{A}$ , $A'$ and $U \setminus A$ . Example: in $U = \mathbb{Z}$ , the complement of the set of even integers is the set of odd integers. The complement of $A^c$ is $A$ , and $A \cup A^c = U$ , $A \cap A^c = \varnothing$ . The complement of $A$ in $U$ is the set difference $U \setminus A$ .

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Element definition
Proposition concept
Set definition
Implication definition
Predicate definition
Universal quantifier definition
Subset definition
Universal set definition
Complement definition

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497 pages build on this one.

Tag	`0B1FSS1VZW`
URI	`m2://0B1FSS1VZW`
Kind	definition
Writing	W1 stated
MSC	03E20
Defines	Complement
Uses	Universal set, Subset, Element

Complement

Definition

Remarks

Reading path

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