Definition:Boolean Algebra/Also defined as
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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 $1.1.2$