Set Complement

The complement of a set is a set of elements not in the set, but in the universal set. By definition all the original set's elements must be part of the universal set. The original set and its complement are both proper subsets of the universal set. Every element in the complementary set is in the universal set, and every element in the original set is in the universal set. No element in the original set is in the complementary set. The number of elements in the complementary set is the difference between the number of elements in the universal set minus the number of elements in the original set.

The complement of the set of numbers (2, 3, 4) if the universal set is defined as the set of numbers (1, 2, 3, 4, 5, 6, 7, 8, 9, 10) is the set (1, 5, 6, 7, 8, 9, 10).

The complement of the set of numbers (1, 2, 3, 4) if the universal set is the set of natural numbers is the set (5, 6, 7, 8 . . .).