What is "de morgan's laws"

n. (plural of De Morgan's law English)

In propositional logic and boolean algebra, De Morgan's laws 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:

The negation of a conjunction is the disjunction of the negations.
The negation of a disjunction is the conjunction of the negations.

or informally as:

"not (A and B)" is the same as "(not A) or (not B)" also, "not (A or B)" is the same as "(not A) and (not B)".

The rules can be expressed in formal language with two propositions P and Q as:

¬(P ∧ Q) ⇔ (¬P) ∨ (¬Q)
and

¬(P ∨ Q) ⇔ (¬P) ∧ (¬Q), 
where:

• ¬ is the negation logic operator (NOT),
•  ∧  is the conjunction logic operator (AND),
•  ∨  is the disjunction logic operator (OR),
•  ⇔  is a metalogical symbol meaning "can be replaced in a logical proof with".

Applications of the rules include simplification of logical expressions in computer programs and digital circuit designs. De Morgan's laws are an example of a more general concept of mathematical duality.