Please help me to define correctly, in the language of mathematics, the configuration of sets shown on the picture. 1. The problem statement, all variables and given/known data I'd like to define the following rules: U is a set with infinite members. L is a list or set of properties. Every property (Ls1, Ls2 ... ) have a value ( 0,1,2,...P ) Every member of U is defined by its unique property list. Every member is paired with one and only one value from each of the Ls1,Ls2... properties. The U contains i+1 subsets. F is a list of functions, or it is the set of subsets of U. Every subset of U is paired with a function in F, except one, which contains all of the members which are not in any subsets defined by F. The subsets of U are determined the following way: An Xk member of U is in subset Fj, ( 1<=j<=i ) if the function Fj outputs "true" after processing the Ls1, Ls2 ... values of Xk. For example: Properties of X0 are: Ls1: 3 Ls2: 2 Ls3: 5 ... Since only the function F1 returns "true" for this input, the X0 is solely in the F1 subset of U. 3. The attempt at a solution I have difficulties even to correctly define the L set and the members of U. Would you please help me to start somehow? Thank you in advance.