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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.
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
HammingDistance  ▪ MatchingDissimilarity  ▪ ...
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