Complement (set theory)

In set theory, the complement of a set A refers to elements not in A. In set theory, the complement of a set A refers to elements not in A. When all sets under consideration are considered to be subsets of a given set U, the absolute complement of A is the set of elements in U but not in A. The relative complement of A with respect to a set B, also termed the difference of sets A and B, written B A, is the set of elements in B but not in A. If A is a set, then the absolute complement of A (or simply the complement of A) is the set of elements not in A. In other words, if U is the universe that contains all the elements under study, and there is no need to mention it because it is obvious and unique, then the absolute complement of A is the relative complement of A in U: