boolalg

A LaTeX package for Boolean algebra: generate truth tables, simplify expressions step-by-step, and prove equivalences directly in your document. Everything runs in pure TeX—no external scripts, Python, or --shell-escape needed.

Quick Start

\usepackage{boolalg}

% Truth table with sub-expressions
\btable{A'B + AB'}

% Step-by-step simplification citing Boolean laws
\bsimplify{(A + B)(A + B')}

% Prove equivalence or find a counterexample
\bprove{A \oplus B = (A + B)(AB)'}
\bprove{A + B = AB}   % prints counterexample: A=0, B=1

Commands

• \btable{<expr>} — Truth table (aliases: \btruth, \truthtable, \btruthtable, \booltruthtable)
• \btable*{<expr>} — Truth table with simplified answer
• \bsimplify{<expr>} — Step-by-step simplification (alias: \boolsimplify)
• \bsimplify*{<expr>} — Final simplified answer only
• \bprove{<lhs> = <rhs>} — Step-by-step proof or counterexample (alias: \boolprove)

Input Syntax (highest to lowest priority)

Variables : Single letters A-Z, a-z
Constants : 0, 1
Grouping  : ( ... )
1. NOT    : not, \lnot, \neg, ', !, ~
2. AND    : AB, *, ., &, and, \land, \wedge, \cdot
   NAND   : nand, \nand, \uparrow, \barwedge
3. OR     : +, |, or, \lor, \vee
   NOR    : nor, \nor, \downarrow
4. XOR    : ^, xor, \xor, \oplus
   XNOR   : xnor, \xnor, \odot, \equiv, \iff

• Examples: AB means A AND B; A' and !A both mean NOT A.
• Note: Put a space after word operators, e.g. "not A".

Settings (override with \def)

\def\boolfname{f}          % Name of the output column (use \empty to hide)
\def\booltablemaxvars{5}   % Skip truth tables with more than 5 variables
\def\boolandsym{\land}     % Customise operator symbols (e.g. \def\boolandsym{\land})

Documentation

See boolalg-doc.pdf for the compiled reference manual and rendered examples.

Author & License

Param Srivastava

Released under the LaTeX Project Public License (LPPL) v1.3c or later.