linguistic:translation
Basic operations

While Elementary algebra has four operations (addition, subtraction, multiplication, and division), the Boolean algebra has only three basic operations: conjunction, disjunction, and negation, expressed with the corresponding binary operators AND (∧ {\displaystyle \land }) and OR (∨ {\displaystyle \lor }) and the unary operator NOT (¬ {\displaystyle \neg }), collectively referred to as boolean operators. Variables in Boolean algebra that store the logical value of 0 and 1 are called the boolean variables. They are used to store either true or false values. The basic operations on boolean variables x and y are defined as follows:

Alternatively, the values of x ∧ y, x ∨ y, and ¬ x can be expressed by tabulating their values with truth tables as follows:

When used in expressions, the operators are applied according to the precedence rules. As with elementary algebra, expressions in parentheses are evaluated first, following the precedence rules.

If the truth values 0 and 1 are interpreted as integers, these operations may be expressed with the ordinary operations of arithmetic (where x + y uses addition and xy uses multiplication), or by the minimum/maximum functions:

One might consider that only negation and one of the two other operations are basic because of the following identities that allow one to define conjunction in terms of negation and the disjunction, and vice versa (De Morgan's laws):