DeMorgan’s Law (also known as DeMorgan’s Rule or DeMorgan’s Theorem) is the most important replacement rule in logic. This lecture explores the first half of it, which says that P ^ Q is equivalent to ~(~P v ~Q). It is really useful because it makes excessively complicated disjuctions with tons of negations into a very clean conjunction, which we can then further dissect.

The rule is named after Augustus De Morgan, a 19th Century British mathematician.