On completeness of multifunction set of rank 2

The problem of completeness of the set of functions from a finite set $A$ to set of all subsets of $A$ is studied. Functions of this kind are called multifunctions on $A$, they generalize the well-known class of functions of $k$-valued logic. The usual superposition adopted for functions of $k$-valued logic is not suitable for multifunctions. In the paper one of the types of superpositions that are commonly used for multifunctions is considered. We prove necessary and sufficient condition for the completeness of an arbitrary set of multifunctions on $\{0, 1\}$ which contains all unary Boolean functions with respect to given superposition.