Boolean algebra

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In mathematics and mathematical logic,
Boolean algebra is the branch of algebra in which the values of the variables are
the truth values true and false, usually denoted 1 and 0, respectively.[1]
Instead of elementary algebra, where the values of the variables are numbers
and the prime operations are addition and multiplication,
the main operations of Boolean algebra are the conjunction (and) denoted as ∧,
the disjunction (or) denoted as ∨, and the negation (not) denoted as ¬.

It is thus a formalism for describing logical operations,
in the same way that elementary algebra describes numerical operations.

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In propositional logic and Boolean algebra,
De Morgan's laws[1][2][3] 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 disjunction is the conjunction of the negations; and
the negation of a conjunction is the disjunction of the negations;
or

the complement of the union of two sets is the same as the intersection of their complements; and
the complement of the intersection of two sets is the same as the union of their complements.
or

not (A or B) = not A and not B; and
not (A and B) = not A or not B