On some $S_I^*$-precomplete sets of multifunctions of rank 2

In this paper, we consider multifunctions defined on a two-element set and returning subsets of a given set as values. We discuss the question of describing all sets that are precomplete with respect to the superposition operation. We give examples of two precomplete sets described in the language of predicate preservation by function; their closedness and precompleteness with respect to the closure under consideration are proved, and an example of a complete set is given.