Definition
Complement of a set
The complement of a set contains everything in the chosen universal set that is not in that set.
What it means
First decide the universe: everything allowed in the discussion. Then mark the set you care about. Its complement is what remains inside the universe but outside that set. Change the universe, and the complement may change too.
Remember it
Inside the universe box, outside the set circle.
Example
Let U = {1, 2, 3, 4, 5, 6} and let A = {2, 4, 6}. The elements of U that are not in A are 1, 3, and 5, so the complement of A is {1, 3, 5}.
Watch for
A complement is not fully determined until the universal set is specified.
Common mix-up
The complement of A is a special set difference: it is U minus A, not A minus U.
Exact meaning
For a set A contained in a specified universal set U, the complement of A is the set of all elements of U that are not elements of A; equivalently, it is the set difference U minus A.