Hyperoperations on {0, 1, 2} based on Min, Max, and Universal Literal operations

This paper will discuss functions with hyperstructure based on Min, Max, and Universal Literal operations on {0, 1, 2}. These three types of operations will be expanded into operations on the set P₃ of non-empty subsets of {0, 1, 2}. Then, the paper will define a special type of compositions, called formulas, and will show a necessary and sufficient condition for a function on P₃ to be expressed by a formula.