False (logic) - in Classical Logic and Boolean Logic

In Classical Logic and Boolean Logic

Boolean logic defines the false in both senses mentioned above: "0" is a propositional constant, whose value by definition is 0. In a classical propositional calculus, depending on the chosen set of fundamental connectives, the false may or may not have a dedicated symbol. Such formulas as p ∧ ¬p and ¬(p → p) may be used instead.

In both systems the negation of the truth gives false. The negation of false is equivalent to the truth not only in classical logic and Boolean logic, but also in most other logical systems, as explained below.