De Morgan's laws
Negating an "and" gives an "or" of negations, and vice versa.
De Morgan's laws state that ¬(A ∧ B) ≡ ¬A ∨ ¬B and ¬(A ∨ B) ≡ ¬A ∧ ¬B. A negation cannot simply be pushed inside a conjunction or disjunction; it switches the connective.
Examples
"Not both cheap and fast" means "not cheap or not fast."
See also