Changes

The first order of business is to define the space in which the relations <math>L_0\!</math> and <math>L_1\!</math> take up residence.  This space is constructed as a 3-fold [[cartesian power]] in the following way.

The first order of business is to define the space in which the relations <math>L_0\!</math> and <math>L_1\!</math> take up residence.  This space is constructed as a 3-fold [[cartesian power]] in the following way.

The ''[[boolean domain]]'' is the set <math>\mathbb{B} = \{ 0, 1 \}.</math> The plus sign <math>^{\backprime\backprime} + ^{\prime\prime},</math> used in the context of the boolean domain <math>\mathbb{B},</math> denotes addition mod 2.  Interpreted for logic, this amounts to the same thing as the boolean operation of ''[[exclusive disjunction|exclusive or]]'' or ''not equal to''.

The ''[[boolean domain]]'' is the set <math>\mathbb{B} = \{ 0, 1 \}.</math>

 

The ''plus sign'' <math>^{\backprime\backprime} + ^{\prime\prime},</math> used in the context of the boolean domain <math>\mathbb{B},</math> denotes addition modulo 2.  Interpreted for logic, the plus sign can be used to indicate either the boolean operation of ''[[exclusive disjunction]]'', <math>\operatorname{XOR} : \mathbb{B} \times \mathbb{B} \to \mathbb{B},</math> or the boolean relation of ''logical inequality'', <math>\operatorname{NEQ} \subseteq \mathbb{B} \times \mathbb{B}.</math>

The third cartesian power of <math>\mathbb{B}</math> is the set <math>\mathbb{B}^3 = \mathbb{B} \times \mathbb{B} \times \mathbb{B} = \{ (x_1, x_2, x_3) : x_j \in \mathbb{B} ~\text{for}~ j = 1, 2, 3 \}.</math>

The third cartesian power of <math>\mathbb{B}</math> is the set <math>\mathbb{B}^3 = \mathbb{B} \times \mathbb{B} \times \mathbb{B} = \{ (x_1, x_2, x_3) : x_j \in \mathbb{B} ~\text{for}~ j = 1, 2, 3 \}.</math>