¬(a ∧ b) = (¬a) ∨ (¬b) and ¬(a ∨ b) = (¬a) ∧ (¬b).
DeMorgan’s law is very useful in electrical engineering and computer engineering because at the lowest level, there is usually a preference to use and-gates or or-gates. This transformation permits the use of only one of the two (and versus or) gates, plus the not-gate.