In propositional logic and Boolean algebra, De Morgan's laws are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British mathematician. The rules allow the expression of conjunctions and disjunctions purely in terms of each other via negation. The rules can be expressed in English as: * the negation of a disjunction is the conjunction of the negations * the negation of a conjunction is the disjunction of the negations or or * not (A or B) = (not A) and (not B) * not (A and B) = (not A) or (not B), where and where