∪ If P is a given subset of the universal set U, we can define a new set ˜ P called the complement of P as follows: P is the set of all elements of U that are not contained in P. For example, if, as above, Q is the set in which candidate A wins the first two primaries, then ˜ Q is the set {P7, P8, . . . , P36}. The shaded area in Figure is the complement of the set P. Observe that the complement of the empty set ∅ is the universal set U, and also that the complement of the.