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Logic & Boolean Algebra—Wolfram Language Documentation

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• Functions
  • AllTrue
  • And
  • AnyTrue
  • AxiomaticTheory
  • Boole
  • BooleanConvert
  • BooleanFunction
  • BooleanMinimize
  • Equal
  • Equivalent
  • Exists
  • False
  • FindClusters
  • FindEquationalProof
  • FindInstance
  • ForAll
  • FullSimplify
  • HammingDistance
  • Implies
  • MatchingDissimilarity
  • Nand
  • Nearest
  • NoneTrue
  • Nor
  • Not
  • Or
  • ProofObject
  • Reduce
  • Resolve
  • SatisfiableQ
  • True
  • Unequal
  • Xor
• Related Guides
  • Manipulating Equations
  • Assumptions & Domains
  • Theorem Proving
  • Distance & Similarity Measures
  • Bitwise Operations
• Tech Notes
  • Relational and Logical Operators
  • Conditionals
  • Quantifiers

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.

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

BooleanFunction — general Boolean function

BooleanConvert  ▪  BooleanMinimize  ▪  SatisfiableQ  ▪  ...

FullSimplify — simplify logic expressions and prove theorems

ForAll (∀), Exists (∃) — quantifiers

Resolve  ▪  Reduce  ▪  FindInstance

FindEquationalProof — generate representations of proofs in equational logic

ProofObject  ▪  AxiomaticTheory  ▪  ...

Nearest, FindClusters — operate on Boolean vectors

HammingDistance  ▪  MatchingDissimilarity  ▪  ...

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