Abstract
References
- P. R. Halmos, Naive set theory, D. Van Nostrand Company, Inc., New York, 2011.
- J. Ferreirós, Labyrinth of thought: A history of set theory and its role in modern mathematics, Birkhäuser, Basel, 2007.
- D. S. Dummit, R. M. Foote, Abstract algebra,Wiley, Hoboken, NJ, 2004.
- T. Hungerford, Algebra, Springer, New York, 2003.
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.
Keywords
Complement of a set Conditional complements Inclusive complement Exclusive complement Complement subgroup
References
- P. R. Halmos, Naive set theory, D. Van Nostrand Company, Inc., New York, 2011.
- J. Ferreirós, Labyrinth of thought: A history of set theory and its role in modern mathematics, Birkhäuser, Basel, 2007.
- D. S. Dummit, R. M. Foote, Abstract algebra,Wiley, Hoboken, NJ, 2004.
- T. Hungerford, Algebra, Springer, New York, 2003.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Articles |
| Authors | |
| Early Pub Date | December 30, 2021 |
| Publication Date | December 31, 2021 |
| Published in Issue | Year 2021 Volume: 10 Issue: 3 |
