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de Morgan's Laws


Let  union represent "or",  intersection represent "and", and ^' represent "not." Then, for two logical units E and F,

 (E union F)^'=E^' intersection F^'
 (E intersection F)^'=E^' union F^'.

These laws also apply in the more general context of Boolean algebra and, in particular, in the Boolean algebra of set theory, in which case  union would denote union,  intersection intersection, and ^' complementation with respect to any superset of E and F.


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References

Dugundji, J. Topology. Englewood Cliffs, NJ: Prentice-Hall, 1965.Halmos, P. R. Naive Set Theory. New York: Springer-Verlag, 1974.Kelley, J. L. General Topology. New York: Springer-Verlag, 1975.Papoulis, A. Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill, p. 23, 1984.Simpson, R. E. Introductory Electronics for Scientists and Engineers, 2nd ed. Boston, MA: Allyn and Bacon, pp. 540-541, 1987.

Cite this as:

Weisstein, Eric W. "de Morgan's Laws." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/deMorgansLaws.html

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