Conditional complements of sets and their application to group theory

Abstract

Among the most important concepts of mathematics are sets, of which one of the critical concepts is the complement of a set. This work defines two conditional complements of sets as a new concept of set theory, i.e., inclusive complement and exclusive complement. By comparing these two, we then explore the relationships between them. We also apply them to the group theory and define complement subgroup of a group. Finally, we conclude the study with two interesting questions about the subject.

Topics & Concepts