A Study On Bisets

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2022 by IJMTT Journal
Volume-68 Issue-1
Year of Publication : 2022
Authors : K. Karpagam, G. Ramesh
  10.14445/22315373/IJMTT-V68I1P511

MLA

MLA Style: K. Karpagam, G. Ramesh. "A Study On Bisets" International Journal of Mathematics Trends and Technology 68.1 (2022):94-100. 

APA Style: K. Karpagam, G. Ramesh(2022). A Study On Bisets. International Journal of Mathematics Trends and Technology, 68(1), 94-100.

Abstract
The concept of biset is introduced, equality, cardinality, complement, subsets of a biset, union, intersection, symmetric difference of two bisets are defined. We also investigated the concepts of functions on a biset and discussed some of their properties.

Reference

[1] Angelo Margaris, First order Mathematical Logic, 1990.
[2] Dauben, Joseph W.(1979), Georg Cantor: His Mathematics and Philosophy of the Infinite. Boston: Harvard University Press, ISBN 0-691-02447-2.
[3] Dubreil P., and Dubreil-Jacotin, M.L., Lectures on Modern Algebra, Oliver and Boyd., Edinburgh, 1967.
[4] Greub, W.H., Linear Algebra, Fourth Edition, Springer-Verlag, 1974.
[5] Halmos, Paul R. (1960), Naive set Theory, Princeton, N.J.: Van Nostrand ISBN 0-387-90092-6.
[6] Herstein,IN., Topics in Algebra, John Wiley, 1975.
[7] Jain P.K.; Khalil Ahmad; P. Ahuja (1995), Functional Analysis, New Age International( P)Limited, publishers, 1995.
[8] Jose Ferreiro's (1 Nov. 2001)Labyrinth of Thought: A History of set theory and its Role in Modern Mathematics, Springer Science and Business Media, ISBN 978-3-7643-5749-8.
[9] Jose Ferriro's (16 August 2007). Labyrinth of Thought: A History of set theory and its Role in Modern Mathematics ISBN 978-3-7643-8349-7.
[10] Kostrikin, A.I., and Manin, Y.I., Linear Algebra and Geometry, Gordon and Breach Science Publishers, 1989.
[11] Lay, D.C., Linear Algebra and its Applications, Addison Wesley, 2003.
[12] Molodtsov, D.A: Soft set theory- rst results. Comp. and Math. With App.37, 19-31(1999).
[13] Padilla, R., Smarandache Notions Journal, 9 (1998)36-38.
[14] Samuel Goldberg, Probability: An introduction, ISBN 978-0-486-65252-8, 1960.
[15] Smarandache, Florentine, Collected papers II, University of Kishinev Press, Kishinev, 1997.
[16] Stoll, Robert R (1974); Sets, Logic and Axiomatic Theories, W.H.Freeman and company.Pp, ISBN 978071604577.
[17] Stoll, Robert R (1979); set theory and Logic. Mineola, N.Y.: Dover Publications, ISBN 0-486-63829-4.
[18] Thomas H. Cormen; Charles E Leiserson; Ronald L Rivest; Cli ord stein (2001), Introduction to Algorithms, MIT press.p.1070. ISBN 978-0-262-03293-3.
[19] Vasantha Kandasamy, W.B., Bivector spaces, U.Sci. Phy.Sci., 11(1999)186-190.
[20] Vasantha Kandasamy, W.B., Bialgebraic Structures and Smarandache Bialgebraic Structures, Amercian Research Press, Rehoboth, 2003.
[21] Vasantha Kandasamy, W.B., Florentin smarandache, Iianthenral, K.,Introduction to Bimatrices, 2005
[22] Vasantha Kandasamy, W.B.,Florentin Smarandache, Iianthenral, K., Introduction to Linear Bialgebra, sep.2005
[23] Velleman, Daniel, How to prove It: A Structured Approach,Cambridge University Press,(2006) ISBN 0-521-67599-5.
[24] Voyevodin, V.V., Linear Algebra, Mir Publishers, 1983.
[25] Zadeh, L.A., Fuzzy Sets, Inform. and Control, 8, (1965), 338-353.
[26] Zelinksy, D., A First Course in Linear Algebra, Academic Press, 1973. 8

Keywords : Bisets, B-union, B-intersection, B-open and B-closed sets.