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 ORs of ANDs corresponding to disjunctive normal form, with some contractions.
See The Mathematica Book: Section 1.5.6 and Section 3.6.6.
See also: Expand.