Notes
Chapter 10:Processes of Perception and Analysis
Section 11:Traditional Mathematics and Mathematical Formulas
Primitive [Boolean] functions
There are several possible choices of primitive functions that can be combined to represent any Boolean function. In DNFAnd,Or andNot are used.Nand = Not[And[##]] & alone is also sufficient, as shown on page619 and further discussed on page807. (It is indicated by⊼ in the main text.) The functionsAnd,Xor andNot are equivalent toTimes,Plus and1 - # & for variables modulo 2, and in this case algebraic functions likePolynomialReduce can be used for minimization. (See also page1102.)