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A Functional Equation For Implication

Published online by Cambridge University Press:  03 November 2016

R. L. Goodstein
R. L. Goodstein*
Affiliation:
The University of Leicester
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Extract

Since all truth functions in two-valued logic may be represented by polynomials in the arithmetic of residues modulo 2, the question which R. Sibson raises in note 3127 may be expressed in the following form : Find all polynomials Φ(p, q) such that

identically, where p & q is a commutative polynomial which vanishes only when p = q = 0, and p & p = p. Taking p = q = r in (1) we find

Type
Research Article
Information
The Mathematical Gazette , Volume 51 , Issue 375 , February 1967 , pp. 38 - 40
Copyright
Copyright © Mathematical Association 1967

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