In mathematics the complement of a set X, sometimes written X' or Xc, is the set of all the elements in the universe under consideration excluding those in the specified set. So if the current universe is the set of natural numbers and X is the set of even numbers then X' is the set of odd numbers.
In logic the complement of a proposition is the negation of that proposition. For example the complement of "the sun is shining" would be "the sun is not shining". For this reason the unary function in a Boolean algebra is often referred to as the complement operation.