This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)


expands out logical combinations of equations, inequalities, and other functions.
  • LogicalExpand generates ORs of ANDs corresponding to disjunctive normal form, with some contractions.
Expand out logic expressions:
Expand out logic expressions:
Click for copyable input
Represent logic expressions as a disjunction of conjunctions (disjunctive normal form):
Simplify logic expressions:
Expand logic expressions out to forms involving only And, Or, and Not:
Expand out combinations of equations:
Get separate equations for different terms in a series:
Convert multi-argument equations and inequalities to two-argument form:
Expand negations of Element statements:
Prove tautologies:
The output of LogicalExpand is equivalent to the input:
De Morgan's laws:
An expanded Xor of variables will always contain terms:
New in 1