Concept

Absolute Complement

The absolute complement — or simply complement— of a set A contains all the elements in the universal set that do not belong to A. The complement of A can be denoted as A^C or A'. A^C={ x | x /∈ A } The above set can be read as the set of all numbers x such that x is not an element of set A. In a Venn Diagram, the complement of A is shown by coloring the area outside A.
The set A and its complement
For instance, consider the integer numbers as a universal set. If A is the set of positive integers, then the complement of A contains the negative integers and zero. U&={..., - 3,- 2,- 1,0,1,2,3,...} A&={ 1,2,3, ... } A^C&={ 0,- 1,- 2,- 3,... }
Exercises