De Morgan's laws
Also known as DeMorgan’s theorem
pair of transformation rules that are both valid rules of inference
AI overview
De Morgan's laws are a pair of rules that show how to rearrange logical statements by swapping "and" and "or" while flipping what is being negated. They matter because they're fundamental tools in logic and mathematics that help simplify complex statements and solve problems more easily.
AI-generated from the Wikipedia summary — may contain errors.
Article
De Morgan's laws represented with Venn diagrams. In each case, the resultant set is the set of all points in any shade of blue. In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British mathematician. The rules allow the expression of conjunctions and disjunctions purely in terms of each other via negation.
The rules can be expressed in English as: