Boolean Computation
Building on its core symbolic architecture, the Wolfram Language 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, the Wolfram Language 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
Special Boolean Functions
BooleanCountingFunction — 
out of 
variables true
BooleanConsecutiveFunction — consecutive 
out of 
variables true
General Boolean Functions
BooleanFunction — general Boolean function (from IDs, mappings with "don't cares", ...)
BooleanMinterms, BooleanMaxterms — combinations of minterms, maxterms
Conjunction, Disjunction — AND, OR with respect to a list of variables (cf. ∑, ∏)
Predicates on Lists
Boolean Structure
BooleanTable — create a truth vector or general truth table
BooleanVariables — find the variables in a Boolean expression
UnateQ — test whether a Boolean expression is unate (monotone)
Visualization
RulePlot — visualize a Boolean function
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
Iterated Boolean Systems »
CellularAutomaton ▪ TuringMachine ▪ SubstitutionSystem ▪ ShiftRegisterSequence
Bit Vector Operations »
BitAnd ▪ BitOr ▪ BitXor ▪ BitLength ▪ BitShiftLeft ▪ BitSet ▪ ...
Numerical Boolean Computation
Nearest, FindClusters — operate on Boolean vectors