31 lines
730 B
Markdown
31 lines
730 B
Markdown
---
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tags:
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- Logic
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- propositional-logic
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- derivation-rules
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- theorems-axioms-laws
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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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