What is the Complement of a Set?

The complement of a given set say M refers to the elements that are not in set M. There are different types of set complements as discussed below;

Absolute complement

All sets are often considered to be subsets or members of a universal set U. Therefore the absolute complement of set Z is the set of elements in U but not in Z.

Relative complement

Unlike absolute complement, relative complement is between two sets say X and Y. Relative complement refers to a set of elements that are in set X but not in Y. For instance if X={1,2,3,4,5} and Y={4,5,6,7,8} then the complement of set X which is abbreviated by Xc = {1,2,3}.Relative complement is also termed as the difference between two sets and is written as X\Y. It is important to understand that Y U Xc = X \Y