Britannica Sources used in this answer

How is the complement of a set determined within a universal set?

Created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.

In set theory, when the elements under consideration are restricted to a fixed class known as the universal set (or universe, denoted as U), the complement of a subset A is determined by identifying all elements within that universe that are not members of A.1

The complement is typically symbolized as A′ or U − A. Essentially, it consists of every element in the universal set U that does not belong to the set A. For example, if the universal set is defined as the 26 letters of the alphabet, the complement of the set of vowels is the set of all consonants.12