1 Definition

Let A be a subset of X. The complement of A in X (denoted A when the larger set X is clear from context) is the set differenceMathworldPlanetmath XA.

The Venn diagramMathworldPlanetmath below illustrates the complement of A in red.


2 Properties

  • (A)=A

  • =X

  • X=

  • If A and B are subsets of X, then AB=AB, where the complement is taken in X.

3 de Morgan’s laws

Let X be a set with subsets AiX for iI, where I is an arbitrary index-set. In other words, I can be finite, countableMathworldPlanetmath, or uncountable. Then

(iIAi) = iIAi,
(iIAi) = iIAi.
Title complement
Canonical name Complement
Date of creation 2013-03-22 12:18:51
Last modified on 2013-03-22 12:18:51
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 7
Author CWoo (3771)
Entry type Definition
Classification msc 03E99
Related topic DeMorgansLaws