# Logic & Boolean Algebra

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

### Boolean Computation »

BooleanFunction general Boolean function

### Mathematical Logic

FullSimplify simplify logic expressions and prove theorems

ForAll (), Exists () quantifiers

### Automated Theorem Proving »

FindEquationalProof generate representations of proofs in equational logic

### Boolean Vector Operations

Nearest, FindClusters operate on Boolean vectors