De Morgan's laws

De Morgan's laws state that the negation of a logical conjunction is equivalent to a disjunction of the negatives; and the negation of a disjunction is equivalent to the conjunction of the negatives.

In other words:
 * not(P and Q) is equivalent to (not P) or (not Q)
 * not(P or Q) is equivalent to (not P) and (not Q)

In symbols:
 * &not;(P &and; Q) &hArr; (&not;P) &or; (&not;Q)
 * &not;(P &or; Q) &hArr; (&not;P) &and; (&not;Q)