inclusiveness and exclusiveness cases in set theory experimentations

Abstract

The concept of set theory is widely used in our everyday activities. The idea of subsets is to play safe while experimenting with the elements of the parent set (also called universal set, ‘U’), to ensure that each subset is distinct from others (by inclusiveness or exclusiveness of one or more of the elements. The elements are uniquely identified from one another, even when they have at least one common characteristic. In this work, the author constructed models used in handling cases of inclusiveness and exclusiveness of some elements of the universal set in the subsets. Considering the total number of subsets as a sample space of subsets of U, the author also introduced probability models to represent the number of required subsets.