Definition of complement of a set?

Answer 1

S', the complement of a set S, in the context of the universal set U, is the set of all elements of U that are not in S.

It is important to note that a complement is defined only in terms of the universal set. The following, rather crude example illustrates the point. Suppose S is the set of all boys.

Then S' may be the set of all girls if U = youngsters;

or S' = set of all girls, women and men if U = people;

or S' = set of all girls, women, men, dogs, cats, cows, ... if U = mammals; and so on.

As you see, changing U alters S'.