2022-04-23 13:26:53 +01:00
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---
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2022-08-20 13:00:04 +01:00
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categories:
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2022-09-06 13:26:44 +01:00
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- Mathematics
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tags: [logic, theorems]
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2022-04-23 13:26:53 +01:00
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---
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DeMorgan's laws express some fundamental equivalences that obtain between the Boolean [connectives](Truth-functional%20connectives.md):
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## First Law
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> The negation of a conjunction is logically equivalent to the disjunction of the negations of the original conjuncts.
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$$
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\sim (P \& Q) \equiv \sim P \lor \sim Q
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$$
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The equivalence is demonstrated with the following truth-table
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## Second Law
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> The negation of a disjunction is equivalent to the conjunction of the negation of the original disjuncts.
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$$
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\sim (P \lor Q) \equiv \sim P & \sim Q
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$$
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