# 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 $1.1.2$