De Morgan laws
Quick Summary
De Morgan's laws are a pair of dually related theorems in logic that allow for the transformation of statements into alternative, often more convenient, forms. While the concepts were known in the 14th century, Augustus De Morgan thoroughly investigated and mathematically expressed them in the 19th century.1
The laws are:
* The negation of a disjunction is equal to the conjunction of the negations of the alternates. Symbolically: (\neg(p \lor q) \equiv \neg p \land \neg q).1
* The negation of a conjunction is equal to the disjunction of the negations of the original conjuncts. Symbolically: (\neg(p \land q) \equiv \neg p \lor \neg q).1
These laws are fundamental to modern symbolic logic and were a significant contribution to its development, alongside the work of George Boole.12
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