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Huntington Axiom

An axiom proposed by Huntington (1933) as part of his definition of a Boolean algebra,

H(x,y)=!(!x v y) v !(!x v !y)=x,
(1)

where !x denotes NOT and x v y denotes OR. Taken together, the three axioms consisting of (1), commutativity

x v y=y v x
(2)

and associativity

(x v y) v z=x v (y v z),
(3)

are equivalent to the axioms of Boolean algebra.

The Huntington operator can be defined in the Wolfram Language by: 

  Huntington := Function[{x, y}, ! (! x \[Or] y)
    \[Or] ! (! x \[Or] ! y)]

That the Huntington axiom is a true statement in Boolean algebra can be verified by examining its truth table.

xyH(x,y)
TTT
TFT
FTF
FFF

See also

Boolean Algebra, Robbins Algebra, Robbins Axiom, Winkler Conditions, Wolfram Axiom

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References

Huntington, E. V. "New Sets of Independent Postulates for the Algebra of Logic, with Special Reference to Whitehead and Russell's Principia Mathematica." Trans. Amer. Math. Soc. 35, 274-304, 1933.Huntington, E. V. "Boolean Algebra. A Correction." Trans. Amer. Math. Soc. 35, 557-558, 1933.

Referenced on Wolfram|Alpha

Huntington Axiom

Cite this as:

Weisstein, Eric W. "Huntington Axiom." From MathWorld--A Wolfram Web Resource. https://wwn.ikan3.com/7hz2929k26_9nqeuhigsnjcgsjpnuemse/HuntingtonAxiom.html

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