De Morgan's laws

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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:

¬(P ∧ Q) ⇔ (¬P) ∨ (¬Q)
¬(P ∨ Q) ⇔ (¬P) ∧ (¬Q)
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