This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 MATHEMATICA GUIDE Functions »| More About »|Tutorials »
Boolean Computation
Building on its core symbolic architecture, Mathematica gives immediate access to the latest in industrial-strength Boolean computation. With highly general symbolic representations of Boolean functions, with full support for "don't-care" arguments and values, Mathematica provides state-of-the-art Boolean function transformation, minimization, elimination, satisfiability, and analysis, making possible verification, testing, and other applications involving hundreds to hundreds of thousands of variables.
Basic Boolean Operators
And(&&,  ▪ Or(||,  ▪ Not(!, ¬ ▪ Nand( ▪ Nor( ▪ Xor() Xnor( ▪ Implies( ▪ Equivalent( ▪ Majority
True, False symbolic truth values
Boole convert symbolic truth values to 0 and 1
General Boolean Functions
BooleanFunction general Boolean function (from IDs, mappings with "don't cares", ...)
BooleanCountingFunction symmetric Boolean function (counting True values)
BooleanMinterms, BooleanMaxterms combinations of minterms, maxterms
Conjunction, Disjunction AND, OR with respect to a list of variables (cf. , )

Boolean Structure
BooleanTable create a truth vector or general truth table
BooleanVariables find the variables in a Boolean expression
Conversion & Minimization
BooleanConvert convert to a specified format (CNF, DNF, ESOP, NOR, BFF, ...)
BooleanMinimize find a minimal Boolean form
Boolean Function Testing
SatisfiableQ test whether any input to a function can give True
SatisfiabilityCount count how many possible inputs give True
SatisfiabilityInstances find instances of inputs that give True
TautologyQ test whether all possible inputs give True
Predicate Calculus
ForAll (), Exists () — quantify over Boolean variables
Resolve eliminate quantified variables from a Boolean expression
LogicalExpand expand expressions involving Boolean operators and equations

Numerical Boolean Computation
Nearest, FindClusters operate on Boolean vectors
Minimize, Maximize Boolean optimization
TUTORIALS