Definition:Boolean Algebra/Also defined as

Boolean Algebra: Also defined as
Some sources define a Boolean algebra to be what on is called a Boolean lattice.

It is a common approach to define (the) Boolean algebra to be an algebraic structure consisting of:
 * a boolean domain (that is, a set with two elements, typically $\set {0, 1}$)

together with:
 * the two operations addition $+$ and multiplication $\times$ defined as follows:


 * $\begin{array}{c|cc}

+ & 0 & 1 \\ \hline 0 & 0 & 1 \\ 1 & 1 & 0 \\ \end{array} \qquad \begin{array}{c|cc} \times & 0 & 1 \\ \hline 0 & 0 & 0 \\ 1 & 0 & 1 \\ \end{array}$

Hence expositions discussing such a structure are often considered to be included in a field of study referred to as Boolean algebra.

However, on we do not take this approach.

Instead, we take the approach of investigating such results in the context of propositional logic.