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Logic & Boolean Algebra
Mathematica represents Boolean expressions in symbolic form, so they can not only be evaluated, but also be symbolically manipulated and transformed. Incorporating state-of-the-art quantifier elimination, satisfiability, and equational logic theorem proving, Mathematica provides a powerful framework for investigations based on Boolean algebra.
Reference
Logical Operators
And(&&, 
) ▪ Or(||, 
) ▪ Not(!, ¬) ▪ Nand(
) ▪ Nor(
) ▪ Xor(
) ▪ Implies(
) ▪ Equivalent(
) ▪ Equal(==) ▪ Unequal(!=) ▪ ...
True, False — symbolic truth values
Boole — convert symbolic truth values to 0 and 1
Boolean Computation »
BooleanFunction — general Boolean function
BooleanConvert ▪ BooleanMinimize ▪ SatisfiableQ ▪ ...
Mathematical Logic
FullSimplify — simplify logic expressions and prove theorems
ForAll (
), Exists (
) — quantifiers
Resolve ▪ Reduce ▪ FindInstance
Boolean Vector Operations
Nearest, FindClusters — operate on Boolean vectors
