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What is a De Morgan's law?

What is a De Morgan's law? Here are some definitions.

Noun
  1. (mathematics) Either of two laws in formal logic which state that:
    1. The negation of a conjunction is the disjunction of the negations; expressed in propositional logic as: ¬ (𝑝 ∧ π‘ž) ⇔ (Β¬ 𝑝) ∨ (Β¬ π‘ž)
    2. The negation of a disjunction is the conjunction of the negations; expressed in propositional logic as: ¬ (𝑝 ∨ π‘ž) ⇔ (Β¬ 𝑝) ∧ (Β¬ π‘ž)
  2. (mathematics) Either of two laws in set theory which state that:
    1. The complement of a union is the intersection of the complements; as expressed by: (𝐴 βˆͺ 𝐡)β€² = 𝐴′ ∩ 𝐡′
    2. The complement of an intersection is the union of the complements; as expressed by: (𝐴 ∩ 𝐡)β€² = 𝐴′ βˆͺ 𝐡′
  3. (mathematics) Any of various laws similar to De Morgan’s laws for set theory and logic; for example:β€ƒΒ¬βˆ€π‘₯ 𝑃(π‘₯) ⇔ βˆƒπ‘₯ ¬𝑃(π‘₯)
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