This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)
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.
And(&&, )  ▪ Or(||, )  ▪ Not(!, ¬)  ▪ Nand()  ▪ Nor()  ▪ Xor()  ▪ Implies()  ▪ Equal()  ▪ Unequal()  ▪ True  ▪ False
If  ▪ Which  ▪ Piecewise
Boole convert symbolic truth values to 0 and 1
LogicalExpand expand out logical expressions to canonical form
FullSimplify simplify logic expressions and prove theorems
FindInstance find instances where Boolean expressions are satisfied
ForAll () — universal quantifier
Exists () — existential quantifier
Resolve eliminate quantifiers in Boolean and other domains
Nearest, FindClusters operate on Boolean vectors