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In Boolean algebra, Poretsky's law of forms shows that the single Boolean equation ${\displaystyle f(X)=0}$ is equivalent to ${\displaystyle g(X)=h(X)}$ if and only if ${\displaystyle g=f\oplus h}$, where ${\displaystyle \oplus }$ represents exclusive or.

The law of forms was discovered by Platon Poretsky.

See also

• Archie Blake (mathematician)
• Blake–Poretsky law

References

• Poretsky, Platon Sergeevich (1884). "O sposobach reschenija lopgischeskich rawenstw i ob obrathom spocobe matematischeskoi logiki" О способах решения логических равенств и об обратном способе [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]. Collected Reports of Meetings of Physical and Mathematical Sciences Section of Naturalists' Society of Kazan University (in Russian) (2). (NB. This publication is also referred to as "On methods of solution of logical equalities and on inverse method of mathematical logic".)
• Brown, Frank Markham (2012) . "Chapter 3: The Blake Canonical Form". Boolean Reasoning - The Logic of Boolean Equations (reissue of 2nd ed.). Mineola, New York: Dover Publications, Inc. p. 100. ISBN 978-0-486-42785-0.
• Couturat, Louis (1914). The Algebra Of Logic. p. 53, section 0.43.
• Lewis, Clarence Irving (1918). A Survey of Symbolic Logic. p. 145, section 7.15.

External links

• "Transhuman Reflections - Poretsky Form to Solve"

• Boolean algebra