A Functional Equation For Implication
R. L. Goodstein · The Mathematical Gazette · 1967
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