The Wolfram Language 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, the Wolfram Language 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

AllTrue  ▪ AnyTrue  ▪ NoneTrue

Boolean Computation»

BooleanFunction— general Boolean function

BooleanConvert  ▪ BooleanMinimize  ▪ SatisfiableQ  ▪ ...

Mathematical Logic

FullSimplify— simplify logic expressions and prove theorems

ForAll (∀),Exists (∃)— quantifiers

Resolve  ▪ Reduce  ▪ FindInstance

Automated Theorem Proving»

FindEquationalProof— generate representations of proofs in equational logic

ProofObject  ▪ AxiomaticTheory  ▪ ...

Boolean Vector Operations

Nearest,FindClusters— operate on Boolean vectors

HammingDistance  ▪ MatchingDissimilarity  ▪ ...

Related Tech Notes

▪
• Relational and Logical Operators
▪
• Conditionals
▪
• Quantifiers

Related Guides

▪
• Manipulating Equations
▪
• Assumptions & Domains
▪
• Theorem Proving
▪
• Distance & Similarity Measures
▪
• Bitwise Operations

Related Links

• Demonstrations related to Logic & Boolean Algebra (Wolfram Demonstrations Project)
• Wolfram Community: Logic and Boolean Algebra