1. Determine the least upper bound and greatest lower bound for the pair of complex integers a and b in the subset C´ used in the examples.
2. Prove that the set of all subsets of a given set S (called the power set of S) forms a lattice under the relation "subset"
3. Consider a set with elements that are totally ordered by a relation. Does the set form a lattice under that relation? If so, show that it does. If not, give a counterexample.