DeMorgan's rule is yet another rule uv inference used in propositional logic. It's a rather complicated one, so read it carefully.
~(P*Q) = (~P^~Q)
~(P^Q) = (~P*~Q)
In this case, ~ means 'not', * means 'and', and ^ means 'or'.
In everyday language, these read as:
"It is not the case that I have an apple and an orange" is the same as "I don't have an apple, or I don't have an orange"
"It is not the case that I have an apple or and orange" is the same as "I don't have an apple, and I don't have an orange".
DeMorgan's rule is often abbreviated DeM when doing logic problems. It is also known as DeMorgan's Law or DeMorgan's theorem. It is named after the 19th century logician Augustus De Morgan, who was the first to state it formally.
Other rules of inference include Modus Tollens, Modus Ponens, and commutativity.