Definition:Boolean Algebra/Also defined as

Boolean Algebra: Also defined as

Some sources define a Boolean algebra to be what on $\mathsf{Pr} \infty \mathsf{fWiki}$ 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 $\mathsf{Pr} \infty \mathsf{fWiki}$ we do not take this approach.

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

Sources

• 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $1$: Elementary, my dear Watson: $\S 1.1$: You have a logical mind if...: Definition $1.1.2$