Study of Application of De-Morgan’s law in Modern Fields
DOI:
https://doi.org/10.54060/jase.v2i2.10Keywords:
Boolean Algebra, Logic diagram, Conditions, Applications, ProofsAbstract
This paper discusses about the De-Morgan's Law, with both the conditions, the law re-lates the intersection and union of sets through complements. In propositional logic De-Morgan’s Laws relate conjunctions and disjunctions of propositions through nega-tion. Use of the law in Boolean algebra has been demonstrated through logic diagram and application of the law in other fields have been described, the paper also discusses about the law along with some examples to prove the law.
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J. Berman and W. J. Blok, “Stipulations, multivalued logic, and De Morgan algebras,” Uic.edu. [Online]. Available: http://homepages.math.uic.edu/~berman/stip10.pdf. [Accessed: 18-Sep-2022].
A. B. Birula, H. Rasiowa, On the Representation of Quasi-boolean Algebras, Journal of Symbolic Logic, vol. 22, Iss. 4, pp. 259–261, 1957.
J. A. Brzozowski, “A CHARACTERIZATION OF de MORGAN ALGEBRAS,” Int. J. Algebra Comput., vol. 11, no. 05, pp. 525–527, 2001.
J. Barwise, “An introduction to first-order logic,” in HANDBOOK OF MATHEMATICAL LOGIC, Elsevier, 1977, pp. 5–46.
C. Collins and P. M. Postal, “Interclausal NEG raising and the scope of negation,” Glossa, vol. 2, no. 1, p. 29, 2017.
Y. M. Movsisyan and V. A. Aslanyan, “Hyperidentities of De Morgan algebras,” Log. J. IGPL, vol. 20, no. 6, pp. 1153–1174, 2012.
M. Kondo, Characterization theorem of 4-valued De Morgan logic, Mem. Fac. Sci. Eng. Shimane Univ. Ser. B Math. Sci. 31 (1998), 73–80.
J. Bird, “De Morgan’s laws,” in Mathematics Pocket Book for Engineers and Scientists, Routledge, 2019, pp. 259–260.
J. A. Bergstra, I. Bethke, and P. Rodenburg, “A propositional logic with 4 values: true, false, divergent and meaningless,” J. Appl. Non-Classical Logics, vol. 5, no. 2, pp. 199–217, 1995.
S. Blamey, “Partial logic, in: Handbook of Philosophical Logic,” vol. 3, pp. 1–70, 1986.
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Copyright (c) 2022 Ranjini Saha, Dr. Ambrish Pandey
This work is licensed under a Creative Commons Attribution 4.0 International License.
