The
absolute complement — or simply
complement— of a A contains all the in the 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 , the complement of A is shown by coloring the area outside A.
For instance, consider the as a universal set. If A is the set of integers, then the complement of A contains the integers and zero.
U&={..., - 3,- 2,- 1,0,1,2,3,...} A&={ 1,2,3, ... } A^C&={ 0,- 1,- 2,- 3,... }