De Morgan's laws

Augustus De Morgan originally observed that the following relationships hold:

not (P and Q) = (not P) or (not Q)
not (P or Q) = (not P) and (not Q)


When written using Alice logic operators the two expressions given above look like:

!(X && Y) = !X || !Y
!(X || Y) = !X && !Y

De Morgan's laws are used in this lesson to show three different formulations that can be used to solve the same logic problem.