LogicalExpand[expr] expands out expressions containing logical connectives such as && and ||.
LogicalExpand applies distributive laws for logical operations. Example: LogicalExpand[p && !(q || r)].
LogicalExpand generates expressions using Or or And corresponding to disjunctive normal form, with some contractions. See The Mathematica Book on the web: Section 1.5.6 and Section 3.6.6. See also: Expand.