# Poretsky's law of forms

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{{Short description|Theorem in Boolean algebra}}
{{Use dmy dates|date=May 2023|cs1-dates=y}}
{{Use list-defined references|date=May 2023}}
In [Boolean algebra](/source/Boolean_algebra), '''Poretsky's law of forms''' shows that the single Boolean equation <math>f(X)=0</math> is equivalent to <math>g(X)=h(X)</math> if and only if <math>g=f\oplus h</math>, where <math>\oplus</math> represents [exclusive or](/source/exclusive_or).

The law of forms was discovered by [Platon Poretsky](/source/Platon_Poretsky).

==See also==
* [Archie Blake (mathematician)](/source/Archie_Blake_(mathematician))
* [Blake–Poretsky law](/source/Blake%E2%80%93Poretsky_law)

==References==
* {{cite journal |script-title=ru:О способах решения логических равенств и об обратном способе |title=O sposobach reschenija lopgischeskich rawenstw i ob obrathom spocobe matematischeskoi logiki |language=ru |trans-title=On methods of solving logical equalities and the inverse method of mathematical logic. An essay in construction of a complete and accessible theory of deduction on qualitative forms |author-first=Platon Sergeevich |author-last=Poretsky |author-link=Platon Sergeevich Poretsky |journal=Collected Reports of Meetings of Physical and Mathematical Sciences Section of Naturalists' Society of Kazan University |issue<!-- or volume? -->=2 |date=1884}} (NB. This publication is also referred to as "On methods of solution of logical equalities and on inverse method of mathematical logic".)
* {{cite book |title=Boolean Reasoning - The Logic of Boolean Equations |chapter=Chapter 3: The Blake Canonical Form |author-first=Frank Markham |author-last=Brown |author-link=:d:Q112500339 |edition=<!-- 2012 -->reissue of 2nd |publisher=[Dover Publications, Inc.](/source/Dover_Publications%2C_Inc.) |location=Mineola, New York |date=2012 |orig-date=2003, 1990 |isbn=978-0-486-42785-0 |page=100 |url=https://books.google.com/books?id=QPzCAgAAQBAJ&q=%22Poretsky%27s+law+of+forms%22}} [<!-- 1st edition -->http://www2.fiit.stuba.sk/~kvasnicka/Free%20books/Brown_Boolean%20Reasoning.pdf<!-- https://web.archive.org/web/20170416231752/http://www2.fiit.stuba.sk/~kvasnicka/Free%20books/Brown_Boolean%20Reasoning.pdf -->]
* {{cite book |title=The Algebra Of Logic |author-first=Louis |author-last=Couturat |author-link=Louis Couturat |date=1914 |page=53, section 0.43}}
* {{cite book |title=A Survey of Symbolic Logic |author-first=Clarence Irving |author-last=Lewis |author-link=Clarence Irving Lewis |date=1918 |page=145, section 7.15}}

==External links==
* [http://www.transhumanreflections.org/boolean_tools.html "Transhuman Reflections - Poretsky Form to Solve"]

Category:Boolean algebra

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